SOMATH Math Enrichment · Arithmetic · Easy & Medium

30 Arithmetic Practice Questions — SOMATH Math Enrichment

A free 30-question multiple-choice arithmetic practice set from SOMATH Math Enrichment. All questions are pure arithmetic — no geometry, no algebra — covering place value, addition, subtraction, multiplication, division, fractions, decimals, rounding, order of operations, and word problems. Every question has a hidden explanation you can reveal one at a time, or all at once.

· By the SOMATH team · 226 W 79th St, UWS

What's in this practice set

  1. The arithmetic building blocks these questions cover
  2. Easy questions (1–15) — warm-up fluency
  3. Medium questions (16–30) — a small stretch
  4. Show all answers & explanations
  5. How SOMATH Math Enrichment builds these skills

The arithmetic building blocks these questions cover

Every question below tests one of eight foundational arithmetic ideas. These are the ideas that quietly power everything a student does later — algebra, fractions, percents, ratios, geometry, even mental math on the playground. When they're solid, later math feels natural. When they're shaky, everything after feels harder than it needs to be.

1. Place value

A digit's value depends on where it sits. In 3,478, the 4 is worth 400 because it lives in the hundreds place. Reading a number correctly — knowing that 7,205 is "seven thousand two hundred five" — is the foundation of every operation that follows.

2. Addition and subtraction with regrouping

When we add 47 + 36, the ones column adds to 13. We keep the 3 and carry the 1 to the tens column. Subtraction works the same way in reverse: when we can't take a bigger digit from a smaller one, we borrow from the next column over. This is the same idea as trading dimes for pennies.

3. Multiplication as repeated grouping

6 × 8 doesn't mean anything mysterious — it means "6 groups of 8" (or "8 groups of 6"). Once a student sees multiplication as grouping, big numbers stop being scary. 24 × 5 is just (20 × 5) + (4 × 5) = 100 + 20 = 120. Breaking a multiplication into smaller pieces is called the distributive property, and it's one of the most useful tricks in math.

4. Division as sharing (or as the opposite of multiplication)

56 ÷ 7 asks a simple question: "7 times what equals 56?" Since 7 × 8 = 56, the answer is 8. Multiplication and division are two sides of the same coin — every division fact has a matching multiplication fact.

5. Fractions as equal parts of a whole

A fraction like 3/4 means "3 out of 4 equal pieces." Two fractions are equivalent when they name the same amount — 1/2 = 3/6 because doubling the pieces on top and on the bottom cuts each piece in half without changing the total. Comparing fractions with the same bottom number is easy: just look at the tops. Comparing fractions with different bottoms usually means finding a common denominator first.

6. Decimals as another way to write fractions

The digits after the decimal point tell you tenths, hundredths, thousandths. So 0.3 = 3/10, and 0.03 = 3/100. Money makes this concrete: $0.75 is 75 hundredths of a dollar, or 3/4 of a dollar.

7. Rounding and estimation

Estimation is a superpower. Knowing that 396 + 508 is about 900 lets a student catch a wrong answer instantly. The rule for rounding is simple: look at the digit right after the place you're rounding to. If it's 5 or more, round up. If it's 4 or less, round down.

8. Order of operations

In an expression like 7 × 6 + 3, we always multiply before we add. Without a shared rule, everyone would get different answers. Multiplication and division come first (left to right), then addition and subtraction (left to right). Anything in parentheses gets done first of all.

How to use this practice set: Work through the questions on paper or out loud. Try each one before revealing the explanation. When you're stuck, click Show answer under that question — the explanation walks through the thinking, not just the answer. When you're done with all 30, hit Show all answers & explanations at the bottom to review everything at once.

Easy · Questions 1–15

Easy questions (1–15)

These are fluency-level questions — the kind a strong student should be able to do quickly and confidently. If any of these feel hard, that's a signal to strengthen the underlying idea before moving on.

Question 1

What is 47 + 36?

  1. 73
  2. 83
  3. 84
  4. 813

Answer: B — 83

Add the ones first: 7 + 6 = 13. Write down 3 and carry 1. Then the tens: 4 + 3 + 1 (carried) = 8. So 47 + 36 = 83.

Question 2

What is 92 − 58?

  1. 34
  2. 36
  3. 44
  4. 46

Answer: A — 34

You cannot take 8 from 2, so borrow 1 ten. Now 12 − 8 = 4. In the tens place: 8 − 5 = 3. That gives 34.

Question 3

In the number 3,478, what is the value of the digit 4?

  1. 4
  2. 40
  3. 400
  4. 4,000

Answer: C — 400

Reading places from the right: 8 = ones, 7 = tens, 4 = hundreds, 3 = thousands. So the 4 is worth 4 hundreds = 400.

Question 4

What is 6 × 8?

  1. 42
  2. 46
  3. 48
  4. 54

Answer: C — 48

6 × 8 is the same as 8 groups of 6 (or 6 groups of 8). 6 × 8 = 48. A quick way to remember it: 6 × 8 = (5 × 8) + 8 = 40 + 8 = 48.

Question 5

What is 56 ÷ 7?

  1. 6
  2. 7
  3. 8
  4. 9

Answer: C — 8

Ask: 7 times what equals 56? Since 7 × 8 = 56, the answer is 8.

Question 6

Which fraction is equivalent to 1/2?

  1. 2/3
  2. 3/6
  3. 3/4
  4. 4/5

Answer: B — 3/6

Multiply the top and bottom of 1/2 by the same number: 1×3 = 3 and 2×3 = 6, so 1/2 = 3/6. The other choices are all bigger than 1/2.

Question 7

Round 3,847 to the nearest hundred.

  1. 3,800
  2. 3,840
  3. 3,850
  4. 3,900

Answer: A — 3,800

The hundreds digit is 8. Look at the digit to its right (the tens): 4. Because 4 is less than 5, we round down and keep 8 hundreds. So 3,847 rounds to 3,800.

Question 8

What number goes in the blank? 9 × ___ = 63

  1. 6
  2. 7
  3. 8
  4. 9

Answer: B — 7

Divide both sides by 9: 63 ÷ 9 = 7. Check: 9 × 7 = 63. ✓

Question 9

Which decimal equals 3/10?

  1. 0.03
  2. 0.3
  3. 3.0
  4. 3.10

Answer: B — 0.3

Ten-ths sit in the first place after the decimal point. Three tenths is written 0.3.

Question 10

What is 100 − 47?

  1. 43
  2. 53
  3. 63
  4. 57

Answer: B — 53

One quick trick: 100 − 47 is the same as 99 − 47 + 1 = 52 + 1 = 53. Or, count up from 47: 47 → 50 is 3, 50 → 100 is 50, total 53.

Question 11

Order these fractions from smallest to largest: 1/4, 1/2, 1/3

  1. 1/2, 1/3, 1/4
  2. 1/4, 1/3, 1/2
  3. 1/3, 1/4, 1/2
  4. 1/4, 1/2, 1/3

Answer: B — 1/4, 1/3, 1/2

When the top numbers (numerators) are all 1, the fraction with the biggest bottom number is the smallest piece. 1/4 < 1/3 < 1/2.

Question 12

What is 25 + 25 + 25 + 25?

  1. 75
  2. 80
  3. 100
  4. 125

Answer: C — 100

This is 4 groups of 25, which is the same as 4 × 25 = 100. Or think about money: 4 quarters = $1.00 = 100 cents.

Question 13

Which sign makes the statement true? 5,208 ___ 5,280

  1. <
  2. >
  3. =
  4. ×

Answer: A — <

Compare place by place. Thousands and hundreds are the same (5,2__). In the tens place, 0 < 8, so 5,208 is less than 5,280.

Question 14

What is 7 × 6 + 3?

  1. 42
  2. 45
  3. 63
  4. 60

Answer: B — 45

Follow the order of operations — multiply first, then add. 7 × 6 = 42, and 42 + 3 = 45.

Question 15

What is half of 48?

  1. 16
  2. 22
  3. 24
  4. 28

Answer: C — 24

Half of a number means divide it by 2. 48 ÷ 2 = 24. Check: 24 + 24 = 48. ✓

Medium · Questions 16–30

Medium questions (16–30)

These take a little more thinking — larger numbers, multiple steps, a word problem or two, and questions that combine ideas. If a student gets 12+ out of 15 correct here without help, they're ready for the next level.

Question 16

What is 348 + 276?

  1. 514
  2. 524
  3. 614
  4. 624

Answer: D — 624

Ones: 8 + 6 = 14, write 4, carry 1. Tens: 4 + 7 + 1 = 12, write 2, carry 1. Hundreds: 3 + 2 + 1 = 6. Answer: 624.

Question 17

What is 1,000 − 468?

  1. 432
  2. 522
  3. 532
  4. 542

Answer: C — 532

Trick: subtract from 999 first, then add 1. 999 − 468 = 531, then 531 + 1 = 532. Or borrow across the zeros: 1,000 − 468 = 532.

Question 18

What is 24 × 5?

  1. 100
  2. 115
  3. 120
  4. 125

Answer: C — 120

Break 24 into 20 + 4. Then (20 × 5) + (4 × 5) = 100 + 20 = 120.

Question 19

What is 144 ÷ 12?

  1. 11
  2. 12
  3. 13
  4. 14

Answer: B — 12

Ask: 12 times what equals 144? Since 12 × 12 = 144, the answer is 12.

Question 20

Which of these is equal to 3/4?

  1. 6/12
  2. 9/12
  3. 8/12
  4. 7/12

Answer: B — 9/12

Multiply the top and bottom of 3/4 by 3: 3 × 3 = 9 and 4 × 3 = 12. So 3/4 = 9/12.

Question 21

What is 2/5 + 1/5?

  1. 2/10
  2. 3/5
  3. 3/10
  4. 1/2

Answer: B — 3/5

When fractions have the same bottom number (denominator), just add the top numbers (numerators). 2 + 1 = 3, so the answer is 3/5. Keep the bottom the same.

Question 22

What is 0.5 + 0.25?

  1. 0.30
  2. 0.55
  3. 0.75
  4. 0.85

Answer: C — 0.75

Line up the decimal points. 0.50 + 0.25 = 0.75. In money: 50 cents + 25 cents = 75 cents.

Question 23

What is 3/10 written as a decimal?

  1. 0.003
  2. 0.03
  3. 0.3
  4. 3.1

Answer: C — 0.3

Tenths are the first place after the decimal point. Three tenths = 0.3. Watch the trap: 0.03 is three hundredths, not three tenths.

Question 24

Estimate: 396 + 508. Which is closest?

  1. 800
  2. 900
  3. 1,000
  4. 1,100

Answer: B — 900

Round each to the nearest hundred: 396 rounds to 400 and 508 rounds to 500. 400 + 500 = 900. (The exact answer is 904, so 900 is closest.)

Question 25

A pack of markers has 6 markers. How many markers are in 8 packs?

  1. 14
  2. 42
  3. 46
  4. 48

Answer: D — 48

This is a multiplication problem: 8 packs × 6 markers per pack = 48 markers.

Question 26

A book has 120 pages. If Maya reads 15 pages a day, how many days will it take her to finish?

  1. 6 days
  2. 7 days
  3. 8 days
  4. 9 days

Answer: C — 8 days

Divide the total pages by pages per day: 120 ÷ 15 = 8. Maya will finish in 8 days.

Question 27

What is 4 × 25 × 3?

  1. 150
  2. 200
  3. 250
  4. 300

Answer: D — 300

Multiplication can be rearranged. 4 × 25 = 100 first (easy trick), then 100 × 3 = 300.

Question 28

Which fraction is greater: 2/3 or 3/5?

  1. 2/3
  2. 3/5
  3. They are equal
  4. You cannot tell

Answer: A — 2/3

Give them a common bottom number. 2/3 = 10/15 and 3/5 = 9/15. Since 10/15 > 9/15, we know 2/3 > 3/5.

Question 29

What is 7,205 rounded to the nearest thousand?

  1. 7,000
  2. 7,200
  3. 7,300
  4. 8,000

Answer: A — 7,000

The thousands digit is 7. The digit to its right (hundreds) is 2, which is less than 5, so round down. 7,205 rounds to 7,000.

Question 30

What is 63 ÷ 9 + 5 × 2?

  1. 17
  2. 16
  3. 19
  4. 21

Answer: A — 17

Order of operations: do multiplication and division before addition. 63 ÷ 9 = 7, and 5 × 2 = 10. Now add: 7 + 10 = 17.

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How SOMATH Math Enrichment builds these skills

At SOMATH, we don't hand kids a worksheet and hope. Every one of the ideas above is taught out loud, in a small group of six or fewer, with a live teacher watching how each student thinks. When a student says "6 × 8 = 48," we ask them why. When they say "I don't know," we back up and rebuild the piece that's missing — usually one specific idea, not the whole topic.

This is what math enrichment looks like when it's done well:

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