Kid Einsteins · Class 12 · Grades 3–4

Kid Einsteins Class 12: Subtracting Fractions with Like Denominators

11 illustrated SOMATH posters, theory for every concept, 55 practice questions, and 10 bonus word problems from easy to challenge. Every question has a click-to-reveal worked solution.

· By SOMATH · Class 12 of 48

How do you subtract fractions with like denominators?

Subtract the numerators, keep the common denominator, then simplify. For example, 7/8 − 3/8 = 4/8 = 1/2. We count how many same-sized pieces remain; we do not subtract the piece sizes.

This lesson connects pictures, equations, and number lines so students can explain why the rule works, not only remember it.

SOMATH Kid Einsteins · Grades 3–4

Build on Class 11: from adding to subtracting fractions

This is Class 12 of the Kid Einsteins course at School of Math, 226 W 79th St, 1st Floor, Upper West Side, New York, NY 10024. Call (646) 668-6151, book a free evaluation, or view the schedule.

Before starting, review Class 11: adding fractions with like denominators. Next comes Class 13: decimals to the tenths and hundredths.

How to use this class: Read a poster, explain the idea aloud, then work the five questions on paper before opening solutions. Use the 10 bonus word problems for extension or homework. All answers start hidden; no PDF is needed.

What does subtracting fractions mean?

Poster 1 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: What does subtracting fractions mean?.
Poster 1: What does subtracting fractions mean?. Select the poster to view it full-size.

Theory and worked example

Subtraction can mean taking away an amount or finding the difference between two amounts. The numerator counts the equal parts you have; the denominator names how many equal parts make one whole.

Start with five sevenths, remove two sevenths, and three sevenths remain: 5/7 − 2/7 = 3/7. Say it in words before writing the equation: “Five seventh-sized pieces minus two seventh-sized pieces leaves three seventh-sized pieces.”

All fractions in one story must refer to the same-sized whole. Circle drawings are schematic: when you draw your own, make the pieces equal. A seven-part bar is often easier to partition accurately than a circle.

Five practice questions

Q1. You have 4 of the 5 equal pieces of a paper strip. Remove 1 piece. What fraction of the original strip remains?

Answer
Start with 4/5. Remove 1/5. Four pieces minus one piece leaves three fifth-sized pieces: 4/5 − 1/5 = 3/5.

Q2. Subtract and simplify: 7/9 − 2/9.

Answer
The pieces are the same size: each is 1/9 of the whole. Subtract the counts: 7 − 2 = 5. Keep the denominator: 7/9 − 2/9 = 5/9. Check by adding the amount removed back to the difference: 5/9 + 2/9 = 7/9.

Q3. Subtract and simplify: 3/4 − 1/4.

Answer
The pieces are the same size: each is 1/4 of the whole. Subtract the counts: 3 − 1 = 2. Keep the denominator: 3/4 − 1/4 = 2/4. Simplify 2/4 to 1/2 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 2/4 + 1/4 = 3/4.

Q4. Which story matches 6/8 − 2/8? A. Start with six eighths and add two eighths. B. Start with six eighths and remove two eighths. C. Start with two eighths and remove six eighths.

Answer
B. The first fraction is the starting amount and the minus sign means take away the second amount. Six eighths minus two eighths leaves four eighths, or 1/2.

Q5. Can you subtract 1/6 of a small paper sheet from 4/6 of a large paper sheet just by counting pieces? Explain.

Answer
No. The sixths are not the same area when the sheets are different sizes. First use a common-sized whole or a common measurement unit; matching denominators alone do not make differently sized sheets comparable.

Same denominator, same-sized parts

Poster 2 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Same denominator, same-sized parts.
Poster 2: Same denominator, same-sized parts. Select the poster to view it full-size.

Theory and worked example

Like denominators are equal denominators. In 5/8 and 3/8, both fractions count eighths of the same whole. Think of the denominator as the name of the unit: apples with apples, centimeters with centimeters, eighths with eighths.

The poster's equal-sized circles each have eight equal parts. Five shaded eighths and three shaded eighths differ by two eighths: 5/8 − 3/8 = 2/8 = 1/4.

If the denominators differ, stop. The pieces need to be renamed with a common denominator before subtracting their counts. That is a later lesson; today we focus on like denominators.

Five practice questions

Q6. Which pair has like denominators? A. 3/5 and 2/5. B. 3/5 and 3/7. C. 1/4 and 1/8.

Answer
A. Both denominators are 5, so both fractions count fifths. Matching numerators in B or C do not make the piece sizes equal.

Q7. In 7/10 − 4/10, what size is each piece?

Answer
Each piece is one tenth, or 1/10, of the same whole. Subtracting the counts gives three tenth-sized pieces: 3/10.

Q8. Subtract and simplify: 9/11 − 2/11.

Answer
The pieces are the same size: each is 1/11 of the whole. Subtract the counts: 9 − 2 = 7. Keep the denominator: 9/11 − 2/11 = 7/11. Check by adding the amount removed back to the difference: 7/11 + 2/11 = 9/11.

Q9. Two equal-sized bars are divided into 6 equal parts each. One has 5 parts shaded and the other has 2. Write their difference.

Answer
The fractions are 5/6 and 2/6. The difference is (5 − 2)/6 = 3/6 = 1/2 of a bar.

Q10. A rectangle has four unequal pieces. May you label each piece 1/4 just because there are four?

Answer
No. Fourths must be equal in area. Four pieces of different sizes are not four equal fourths; redraw the whole in four equal-area parts.

Subtract the numerators

Poster 3 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Subtract the numerators.
Poster 3: Subtract the numerators. Select the poster to view it full-size.

Theory and worked example

Once the denominators match, subtract the top numbers. For 6/7 − 2/7, work out 6 − 2 = 4, then write 4/7. You removed two of the six seventh-sized pieces.

The general rule is a/d − b/d = (a − b)/d, where d is positive. In this class we use starting amounts at least as large as the amounts removed, so the differences are not negative.

Subtract in the order written. Do not reverse the numbers merely to get an answer you like. Check the result with addition: 4/7 + 2/7 = 6/7.

Five practice questions

Q11. Subtract and simplify: 10/11 − 3/11.

Answer
The pieces are the same size: each is 1/11 of the whole. Subtract the counts: 10 − 3 = 7. Keep the denominator: 10/11 − 3/11 = 7/11. Check by adding the amount removed back to the difference: 7/11 + 3/11 = 10/11.

Q12. Subtract and simplify: 8/9 − 3/9.

Answer
The pieces are the same size: each is 1/9 of the whole. Subtract the counts: 8 − 3 = 5. Keep the denominator: 8/9 − 3/9 = 5/9. Check by adding the amount removed back to the difference: 5/9 + 3/9 = 8/9.

Q13. Subtract and simplify: 11/12 − 4/12.

Answer
The pieces are the same size: each is 1/12 of the whole. Subtract the counts: 11 − 4 = 7. Keep the denominator: 11/12 − 4/12 = 7/12. Check by adding the amount removed back to the difference: 7/12 + 4/12 = 11/12.

Q14. Subtract and simplify: 9/10 − 7/10.

Answer
The pieces are the same size: each is 1/10 of the whole. Subtract the counts: 9 − 7 = 2. Keep the denominator: 9/10 − 7/10 = 2/10. Simplify 2/10 to 1/5 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 2/10 + 7/10 = 9/10.

Q15. Fill the blank: 8/11 − □/11 = 3/11.

Answer
Work with the numerators: 8 − □ = 3. The missing count is 5, so the missing fraction is 5/11. Check: 3/11 + 5/11 = 8/11.

Keep the denominator the same

Poster 4 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Keep the denominator the same.
Poster 4: Keep the denominator the same. Select the poster to view it full-size.

Theory and worked example

Taking away pieces changes how many pieces remain, not the original size of each piece. After 6/7 − 2/7, the remaining pieces are still sevenths. The answer before simplifying is 4/7, not 4/0 and not 4/14.

Never subtract the denominators. A denominator of zero does not describe a valid fraction. You also do not add the denominators when subtracting.

“Keep the denominator” describes the subtraction step. You may then simplify the result by dividing both numerator and denominator by the same nonzero common factor. For example, 6/8 − 2/8 = 4/8 = 1/2.

Five practice questions

Q16. A student writes 8/9 − 1/9 = 7/0. Correct the error.

Answer
The student subtracted the denominators. Subtract only the numerators: 8 − 1 = 7. The pieces remain ninths, so the answer is 7/9. A fraction cannot have denominator 0.

Q17. Complete: 9/12 − 5/12 = 4/□. Then simplify.

Answer
The blank is 12 because the pieces are twelfths. The difference is 4/12. Divide top and bottom by 4 to get 1/3.

Q18. Subtract and simplify: 7/8 − 3/8.

Answer
The pieces are the same size: each is 1/8 of the whole. Subtract the counts: 7 − 3 = 4. Keep the denominator: 7/8 − 3/8 = 4/8. Simplify 4/8 to 1/2 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 4/8 + 3/8 = 7/8.

Q19. Why does 5/9 − 2/9 not equal 3/18?

Answer
Subtracting does not cut each ninth into smaller pieces. You have 5 − 2 = 3 ninths, so the answer is 3/9 = 1/3, not 3/18.

Q20. For 8/10 − 3/10, which remains unchanged during subtraction: the count of pieces or the size of each piece?

Answer
The size of each piece stays unchanged at 1/10. The count changes from 8 to 5, so the difference is 5/10 = 1/2.

Model subtraction with fraction bars

Poster 5 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Model subtraction with fraction bars.
Poster 5: Model subtraction with fraction bars. Select the poster to view it full-size.

Theory and worked example

Draw one rectangle and split it into equal-width sections. Shade the starting numerator, cross out the amount removed, and count the shaded sections that remain. Keep the outline of the original whole visible.

The poster uses seven equal sections: shade five, cross out two of those five, and count three left. The equation is 5/7 − 2/7 = 3/7.

Use the same-length bar if you draw the start, removed amount, and result separately. Do not shorten the whole when shading less of it. For your written work, a single bar with crossed-out pieces makes the take-away action especially clear.

Five practice questions

Q21. Draw a bar with 8 equal sections. Shade 7 and cross out 3 of the shaded sections. Write and simplify the result.

Answer
Seven eighths minus three eighths leaves four shaded eighths: 7/8 − 3/8 = 4/8 = 1/2.

Q22. A bar has 10 equal sections with 9 shaded. Cross out 4. How many sections and what fraction remain?

Answer
9 − 4 = 5 sections remain shaded. Each is one tenth of the original bar, so 5/10 = 1/2 remains.

Q23. Draw a model for 4/6 − 1/6.

Answer
Divide a bar into six equal sections. Shade four and cross out one shaded section. Three remain: 4/6 − 1/6 = 3/6 = 1/2.

Q24. A bar of 12 equal sections ends with 5 shaded after 4 shaded sections were crossed out. What was the starting fraction?

Answer
Add the removed amount back: 5 + 4 = 9 sections were shaded at the start. The starting fraction was 9/12 = 3/4; 9/12 − 4/12 = 5/12.

Q25. A child cuts away 3 shaded sections from a bar originally divided into 10 equal sections. Four shaded sections remain. The child calls the remaining shaded amount 4/7. What fraction of the original whole is shaded?

Answer
The reference whole is still the original ten-section bar. Four original tenth-sized sections remain shaded, so the answer is 4/10 = 2/5. The fraction 4/7 describes the smaller piece of bar, not the original whole.

Model subtraction with circles

Poster 6 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Model subtraction with circles.
Poster 6: Model subtraction with circles. Select the poster to view it full-size.

Theory and worked example

A circle can represent one whole pizza or one whole pie. Equal fractions require equal-area sectors. Use a prepared fraction circle or draw halves, fourths, or eighths carefully; treat the poster's seventh-sized sectors as a schematic picture, not a measuring template.

For the poster's equation, imagine seven equal sectors, shade five, and remove two shaded sectors. Three sevenths remain. The number of equal sectors in the original whole stays seven.

The shape may change from bar to circle, but the mathematics does not. 5/7 − 2/7 = 3/7 in either model because the same fraction units are being counted.

Five practice questions

Q26. A circle has 4 equal sectors. Shade 3, then cross out 1 shaded sector. What fraction remains?

Answer
3/4 − 1/4 = 2/4 = 1/2. Two of the original four equal sectors remain shaded.

Q27. A circle has 8 equal sectors. Shade 6 and remove 2 shaded sectors. Simplify the remainder.

Answer
6/8 − 2/8 = 4/8. Four eighths cover half the circle, so the simplest form is 1/2.

Q28. Model 5/6 − 2/6 with a circle. Describe your drawing.

Answer
Use six equal-area sectors. Shade five, cross out two shaded sectors, and leave three shaded. The equation is 5/6 − 2/6 = 3/6 = 1/2.

Q29. Two same-sized circles have 8 equal sectors each. One has 7 shaded and the other has 3. How much greater is the first shaded amount?

Answer
Find the difference: 7/8 − 3/8 = 4/8 = 1/2 of a circle. This is a comparison, rather than a physical removal, but subtraction works the same way.

Q30. Show 11/12 − 4/12 with both a circle and a bar. Should the two models give different fraction answers?

Answer
No. Divide each model into twelve equal parts, shade eleven, and cross out four shaded parts. Both models leave seven twelfths: 11/12 − 4/12 = 7/12. The shape of the model does not change the fraction calculation.

Model fractions with shaded sets

Poster 7 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Model fractions with shaded sets.
Poster 7: Model fractions with shaded sets. Select the poster to view it full-size.

Theory and worked example

The whole does not have to be a single connected shape. In this poster, the full set of seven hexagons is one whole set. Five selected hexagons represent 5/7 of that set.

Remove two of the five selected hexagons and three selected hexagons remain: 5/7 − 2/7 = 3/7 of the original set. The denominator counts the original seven objects, not the number currently selected.

This is a counting model: each object contributes one equal counting unit. The yellow pair shows how many to remove; to show the action on a single drawing, cross out two originally green hexagons.

Five practice questions

Q31. A set has 9 identical counters. Seven are selected. Remove 2 selected counters. What fraction of the original set remains selected?

Answer
The original whole set has 9 counters. Seven selected minus two selected leaves five selected: 7/9 − 2/9 = 5/9.

Q32. Six of 8 stars are colored. Erase the color from 2 stars. What fraction stays colored?

Answer
6/8 − 2/8 = 4/8 = 1/2 of the original eight-star set.

Q33. A set contains 12 beads. Ten are in a chosen group. Move 4 out of that group. Write and simplify the change.

Answer
The group changes from 10/12 of the original set to (10 − 4)/12 = 6/12 = 1/2. All fractions still use the original 12 beads as the whole.

Q34. After 3 of 6 selected counters are removed, 3 remain. The original set had 7 counters. Is the remaining selected fraction 3/4 or 3/7?

Answer
It is 3/7 of the original set. The equation is 6/7 − 3/7 = 3/7. The denominator stays tied to the original seven counters.

Q35. A set of 10 counters has 4 still selected after 3 selected counters were removed. What fraction was selected at the start?

Answer
Add back the removed counters: 4 + 3 = 7 selected initially. The starting fraction was 7/10. Check: 7/10 − 3/10 = 4/10.

Subtract on a number line

Poster 8 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Subtract on a number line.
Poster 8: Subtract on a number line. Select the poster to view it full-size.

Theory and worked example

Divide the interval from 0 to 1 into equal steps. On a sevenths line, each step is 1/7. Start at the first fraction and move left by the amount you subtract.

To model 5/7 − 2/7, start at 5/7 and move two steps left: first to 4/7, then to 3/7. The landing point is the difference. Count the spaces between tick marks, not the number of marks you touch.

The whole interval from 0 to 1 has seven steps but eight tick marks, including both endpoints. Subtracting zero means no movement; subtracting the full starting amount lands at zero.

Five practice questions

Q36. On a line marked in eighths, start at 7/8 and move left 3 steps. Where do you land?

Answer
The steps are 7/8 → 6/8 → 5/8 → 4/8. You land at 4/8 = 1/2, so 7/8 − 3/8 = 1/2.

Q37. On a line marked in tenths, start at 9/10 and subtract 4/10. Give the direction, number of steps, and landing point.

Answer
Move left four one-tenth steps: 8/10, 7/10, 6/10, 5/10. The landing point is 5/10 = 1/2.

Q38. You move from 6/7 to 2/7. What fraction did you subtract?

Answer
You moved left four seventh-sized spaces, so you subtracted 4/7. Check: 6/7 − 4/7 = 2/7.

Q39. How many equally spaced tick marks, including 0 and 1, are needed to mark a whole in fifths?

Answer
Six marks create five spaces: 0, 1/5, 2/5, 3/5, 4/5, 1. Fractions measure the spaces from zero.

Q40. Start at 5/6 and move left 5 sixth-sized steps. Where do you land?

Answer
The pieces are the same size: each is 1/6 of the whole. Subtract the counts: 5 − 5 = 0. Keep the denominator: 5/6 − 5/6 = 0/6. Zero 6ths means nothing remains, so the answer is 0. Check by adding the amount removed back to the difference: 0/6 + 5/6 = 5/6.

Simplify the difference

Poster 9 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Simplify the difference.
Poster 9: Simplify the difference. Select the poster to view it full-size.

Theory and worked example

First subtract using the common denominator. Then look for a number greater than 1 that divides both the numerator and denominator. Dividing both by their greatest common factor (GCF) writes the answer in simplest form.

For 5/8 − 3/8, subtraction gives 2/8. Divide 2 and 8 by 2 to get 1/4. The amount did not shrink; two small eighths have simply been renamed as one fourth.

Both 2/8 and 1/4 are correct values, but “simplify” asks for 1/4. If the numerator is zero, write 0. If the numerator equals the positive denominator, write 1. Check by adding back the removed amount, using the original denominator if that is easier.

Five practice questions

Q41. Subtract and simplify: 13/16 − 3/16.

Answer
The pieces are the same size: each is 1/16 of the whole. Subtract the counts: 13 − 3 = 10. Keep the denominator: 13/16 − 3/16 = 10/16. Simplify 10/16 to 5/8 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 10/16 + 3/16 = 13/16.

Q42. Subtract and simplify: 9/12 − 3/12.

Answer
The pieces are the same size: each is 1/12 of the whole. Subtract the counts: 9 − 3 = 6. Keep the denominator: 9/12 − 3/12 = 6/12. Simplify 6/12 to 1/2 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 6/12 + 3/12 = 9/12.

Q43. Subtract and simplify: 11/15 − 5/15.

Answer
The pieces are the same size: each is 1/15 of the whole. Subtract the counts: 11 − 5 = 6. Keep the denominator: 11/15 − 5/15 = 6/15. Simplify 6/15 to 2/5 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 6/15 + 5/15 = 11/15.

Q44. Subtract and simplify: 14/20 − 6/20.

Answer
The pieces are the same size: each is 1/20 of the whole. Subtract the counts: 14 − 6 = 8. Keep the denominator: 14/20 − 6/20 = 8/20. Simplify 8/20 to 2/5 by dividing the numerator and denominator by their greatest common factor. Check by adding the amount removed back to the difference: 8/20 + 6/20 = 14/20.

Q45. A student simplifies 6/9 to 2/9 by dividing only the numerator by 3. Explain and correct.

Answer
To preserve the value, divide both numerator and denominator by the same factor. 6 ÷ 3 = 2 and 9 ÷ 3 = 3, so 6/9 = 2/3. Dividing only the top changes the amount.

Word problems about food

Poster 10 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Word problems about food.
Poster 10: Word problems about food. Select the poster to view it full-size.

Theory and worked example

Corrected example: You had 5/7 of a pizza and gave a friend 2/7 of that same whole pizza. What remains? Subtract the amount given away from the amount you had: 5/7 − 2/7 = 3/7 of the pizza.

Track what each action means. Eating and giving away both remove food. If you began with a whole pizza, ate 5/7, and then gave away 2/7, you would have 7/7 − 5/7 − 2/7 = 0 left, not 3/7.

Before calculating, name the starting amount, the amount removed, and the unit. Finish with a sentence such as “There is one fourth of the original cake left,” not just a bare number.

Five practice questions

Q46. You have 7/8 of a pizza and serve 3/8 of the whole pizza. What fraction remains?

Answer
Subtract served from available: 7/8 − 3/8 = 4/8 = 1/2. Half of the original pizza remains.

Q47. There is 5/6 of a cake. Friends eat 2/6 of the whole cake. How much is left?

Answer
5/6 − 2/6 = 3/6 = 1/2. One half of the original cake remains.

Q48. A chocolate bar has 10 equal pieces. You have 8 pieces and give away 3. What fraction of the original bar do you keep?

Answer
You start with 8/10 and give away 3/10. The difference is 5/10 = 1/2 of the original bar.

Q49. A tray starts with 12 equal-sized muffins. Breakfast uses 5 muffins and a snack uses 4. What fraction of the original tray remains?

Answer
Subtract both amounts from the original whole: 12/12 − 5/12 = 7/12, then 7/12 − 4/12 = 3/12 = 1/4. Three muffins, or one fourth of the original tray, remain.

Q50. A container holds 11/12 liter of soup. Lunch uses 4/12 liter and dinner uses 3/12 liter. How much remains?

Answer
Subtract both meals: 11/12 − 4/12 = 7/12, then 7/12 − 3/12 = 4/12 = 1/3 liter. Check: 4/12 + 3/12 + 4/12 = 11/12.

Word problems about distance

Poster 11 of 11 · Kid Einsteins Class 12

SOMATH Class 12 poster: Word problems about distance.
Poster 11: Word problems about distance. Select the poster to view it full-size.

Theory and worked example

“How much farther?” asks for the difference between a target distance and the distance already covered. In the poster, Maya plans 6/8 mile and runs 3/8 mile. She still needs 6/8 − 3/8 = 3/8 mile.

The reference unit is one mile. The diagram shows a 6/8-mile segment split into two 3/8-mile lengths; the entire drawn segment is not one mile. Always read the labels before interpreting the picture.

Use the same rule for lengths of ribbon, amounts of liquid, or time measured in hours. Keep the unit in your final answer, and make sure both measurements use that same unit before subtracting.

Five practice questions

Q51. Owen plans to cycle 11/16 mile and has cycled 5/16 mile. How much farther must he cycle?

Answer
Planned minus completed: 11/16 − 5/16 = 6/16 = 3/8 mile. Check using sixteenths: 5/16 + 6/16 = 11/16 mile.

Q52. A Riverside Park walk is 9/10 mile. You have walked 4/10 mile. How much remains?

Answer
9/10 − 4/10 = 5/10 = 1/2 mile remains. The denominator names tenths of a mile, not tenths of the route.

Q53. A ribbon is 11/12 meter long. You cut off 5/12 meter. How much is left?

Answer
11/12 − 5/12 = 6/12 = 1/2 meter. Half a meter of ribbon remains.

Q54. Lena walks 7/8 mile. Noah walks 5/8 mile. How much farther does Lena walk?

Answer
Compare their distances: 7/8 − 5/8 = 2/8 = 1/4 mile. Lena walks one fourth of a mile farther.

Q55. Your goal is 11/12 mile. You walk 3/12 mile before a break and 4/12 mile afterward. How much farther is needed?

Answer
Completed distance: 3/12 + 4/12 = 7/12 mile. Remaining distance: 11/12 − 7/12 = 4/12 = 1/3 mile.

10 bonus word problems

Easy → medium → hard → challenge

Write an equation, solve, simplify, and label the unit. For multi-step problems, name the amount left after each action before continuing.

W1 (Easy). At an Upper West Side pizza shop, Ava has 5/8 of a pizza. She shares 1/8 of the whole pizza with her brother. What fraction does she keep?

Answer
Identify the starting amount, 5/8, and the amount removed, 1/8. Subtract: 5/8 − 1/8 = 4/8. Divide both numbers by 4: 4/8 = 1/2. Ava keeps half of the original pizza.

W2 (Easy). A craft ribbon at SOMATH measures 7/10 meter. You use 2/10 meter for a bookmark. How much ribbon remains?

Answer
Both lengths are in tenths of a meter. Subtract 7 − 2 = 5 and keep the denominator 10: 5/10 meter. Simplify to 1/2 meter.

W3 (Easy). A toy train track is 13/14 meter long. A train has traveled 5/14 meter from the start. How much farther is the end of the track?

Answer
Remaining = total length − distance traveled. Calculate 13/14 − 5/14 = 8/14 = 4/7 meter. Divide both 8 and 14 by 2 to simplify.

W4 (Medium). A garden watering can holds 11/12 liter. You pour 3/12 liter on flowers and 2/12 liter on herbs. How much remains?

Answer
First remove the flower water: 11/12 − 3/12 = 8/12. Then remove the herb water: 8/12 − 2/12 = 6/12 = 1/2 liter. Check that used plus remaining is 3/12 + 2/12 + 6/12 = 11/12.

W5 (Medium). Milo reads for 7/8 hour on Saturday and 3/8 hour on Sunday. How much longer does he read on Saturday? Give the answer in hours.

Answer
This asks for a comparison, not the total. Subtract 7/8 − 3/8 = 4/8 = 1/2 hour. Saturday's reading is one half hour longer.

W6 (Medium). A juice pitcher has some juice. After you pour out 3/10 liter, 4/10 liter remains. How much juice was there at the start?

Answer
Undo subtraction by adding the removed amount back. Start = remaining + removed = 4/10 + 3/10 = 7/10 liter. Check: 7/10 − 3/10 = 4/10.

W7 (Hard). A Central Park route is 15/16 mile. You walk 5/16 mile before a stop and 4/16 mile afterward. How much of the route is left, in miles?

Answer
Total completed = 5/16 + 4/16 = 9/16 mile. Remaining = 15/16 − 9/16 = 6/16 mile. Divide top and bottom by 2: 6/16 = 3/8 mile.

W8 (Hard). A baker has 13/15 kilogram of dough. She uses 4/15 kilogram for rolls. She needs 6/15 kilogram for a loaf. After making both, how much dough will remain?

Answer
After the rolls: 13/15 − 4/15 = 9/15 kilogram. This is enough for the loaf because 9/15 is greater than 6/15. After the loaf: 9/15 − 6/15 = 3/15 = 1/5 kilogram.

W9 (Challenge). Two same-sized fruit trays each begin with 9/10 of a full tray. From tray A, children eat 2/10 of a full tray. From tray B, they eat 5/10. How much more fruit remains in A than in B?

Answer
Tray A has 9/10 − 2/10 = 7/10 left. Tray B has 9/10 − 5/10 = 4/10 left. Compare the remainders: 7/10 − 4/10 = 3/10. Tray A has three tenths of a full tray more than tray B.

W10 (Challenge). A class has 17/20 liter of paint. The first mural uses 5/20 liter. After a second mural, 4/20 liter remains. How much paint did the second mural use? Was it more or less than the first, and by how much?

Answer
After the first mural, 17/20 − 5/20 = 12/20 liter remains. The second mural uses 12/20 − 4/20 = 8/20 = 2/5 liter. Compare the amounts used: 8/20 − 5/20 = 3/20 liter. The second mural uses 3/20 liter more. Check: 5/20 + 8/20 + 4/20 = 17/20.

Frequently asked questions

How do you subtract fractions with like denominators?
Subtract the numerators, keep the common denominator, then simplify if possible. For example, 7/8 − 3/8 = 4/8 = 1/2. The fractions must refer to the same whole or measurement unit.
Why does the denominator stay the same?
It names the size of each equal part. Taking away two seventh-sized pieces does not change the size of the remaining seventh-sized pieces; it changes their count.
Can the denominator change when I simplify?
Yes. Keep the denominator during subtraction, then divide both the numerator and denominator by the same common factor to simplify. For example, 6/10 − 2/10 = 4/10 = 2/5.
How do I subtract fractions on a number line?
Start at the first fraction and move left by the fraction being subtracted. On a line divided into eighths, 7/8 − 3/8 means three one-eighth steps left, landing at 4/8 = 1/2.
What happens when I subtract a fraction from itself?
The difference is zero. For example, 5/6 − 5/6 = 0/6 = 0. All of the starting amount has been removed.
Do the wholes have to be the same size?
Yes, when counting pieces of a whole. One fourth of a large pizza is not the same amount as one fourth of a small pizza. Measurement problems must likewise use a common unit.
What if the denominators are different?
Rename the fractions with a common denominator before subtracting. This class practices like denominators; the later unlike-denominator lesson covers that extra step.
What is included in Kid Einsteins Class 12?
This HTML lesson for grades 3–4 includes 11 supplied SOMATH posters, theory under each poster, 55 practice questions, 10 bonus word problems, and 65 individually hidden worked solutions. The food-poster wording is explicitly corrected in the lesson.

Ready to move on?

You are ready when you can identify the whole, subtract without changing the denominator, draw a model, simplify, and check by addition. If a step is difficult, return to that poster and explain one example in words before trying another question.

Find the right next class at SOMATH

Explore the Kid Einsteins syllabus, check the schedule, or book a free evaluation at 226 W 79th St, Upper West Side. Questions? Call (646) 668-6151.

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