Practice dividing fractions, computing with decimals, and working with GCF, LCM & the distributive property — check every answer right on the page.
Score: 0 / 18
🟢 Easy
1/2 ÷ 1/4 = ? How many quarters fit inside one half?
💡 Hint
How many 1/4 pieces do you stack up to reach exactly 1/2?
Keep–Change–Flip: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Two quarter-pieces fill a half — a quarter is half the size of a half, so exactly two fit. You flip the divisor because dividing by 1/4 asks "how many quarters fit inside?"
0.5 + 0.3 = ?
💡 Hint
Line up the points — what do 5 tenths plus 3 tenths make?
Line up the decimal points: 0.5 + 0.3 = 0.8. Aligning the points keeps tenths with tenths, so 5 tenths + 3 tenths = 8 tenths.
What is the GCF of 8 and 12?
💡 Hint
What is the largest number that divides BOTH 8 and 12 with nothing left over?
Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Biggest shared factor = 4. The GCF is the biggest tile that fits evenly into both numbers.
What is the LCM of 3 and 4?
💡 Hint
Count by 3s and by 4s — what is the first number both lists reach?
Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. Smallest shared multiple = 12. The LCM is the first time the two counting patterns line up.
3/4 ÷ 1/8 = ? How many eighths fit inside three-quarters?
💡 Hint
After you flip 1/8, what do you multiply 3/4 by?
Keep–Change–Flip: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. Each whole holds eight eighths, so three-quarters holds six of them.
1.5 − 0.7 = ?
💡 Hint
Line up the points — what is 15 tenths minus 7 tenths?
Line up the points and subtract: 1.5 − 0.7 = 0.8. Aligning place values keeps tenths under tenths, so 15 tenths − 7 tenths = 8 tenths.
🟡 Medium
2/3 ÷ 1/6 = ?
💡 Hint
Keep 2/3, change ÷ to ×, and flip 1/6 to what?
Keep–Change–Flip: 2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4. You flip the divisor because dividing by 1/6 counts how many sixths fit inside 2/3.
1.2 × 0.5 = ?
💡 Hint
Multiply 12 × 5, then place 2 digits after the point.
12 × 5 = 60. There is 1 decimal place in 1.2 and 1 in 0.5, so 2 decimal places total → 0.60 = 0.6. Multiplying by 0.5 is the same as taking half, so the answer is half of 1.2.
What is the GCF of 24 and 36?
💡 Hint
Break each into primes — which primes do 24 and 36 share?
24 = 2·2·2·3 and 36 = 2·2·3·3. Shared primes: 2·2·3 = 12. Multiplying only the primes they share gives the largest factor common to both.
What is the LCM of 6 and 8?
💡 Hint
Take every prime at its highest power across 6 and 8.
6 = 2·3 and 8 = 2·2·2. All primes at highest power: 2·2·2·3 = 24. Taking the highest power of each prime guarantees the result is divisible by both 6 and 8.
Use the distributive property to factor out the GCF of 18 + 24.
💡 Hint
What is the GCF of 18 and 24, and what is left when you divide each by it?
GCF(18, 24) = 6. Then 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18 + 24 = 6 × (3 + 4) = 6 × 7 = 42. ✓ Factoring out the GCF is the distributive property in reverse — 6 groups of 3 plus 6 groups of 4.
4.8 ÷ 0.6 = ?
💡 Hint
Slide both points one place to turn 0.6 into a whole number.
Multiply both by 10 to clear the decimal: 48 ÷ 6 = 8. Scaling both numbers the same way keeps the quotient unchanged; it asks how many 0.6s fit in 4.8.
🔴 Hard
5/6 ÷ 2/3 = ? Give your answer as a fraction or a decimal.
💡 Hint
Flip 2/3 to 3/2, then multiply across and simplify.
Keep–Change–Flip: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1.25. Since 2/3 is less than 1, more than one of it fits inside 5/6, so the answer lands above 1.
325 × 14 = 4550. There are 2 + 1 = 3 decimal places total → 4.550 = 4.55. The trailing zero drops because 4.550 and 4.55 name the same value.
What is the GCF of 48 and 72?
💡 Hint
Break each into primes — multiply only the primes 48 and 72 share.
48 = 2·2·2·2·3 and 72 = 2·2·2·3·3. Shared primes: 2·2·2·3 = 24. Taking each shared prime at the lower of its two powers gives the greatest common factor.
What is the LCM of 12 and 18?
💡 Hint
Take each prime at its highest power across 12 and 18.
12 = 2·2·3 and 18 = 2·3·3. All primes at highest power: 2·2·3·3 = 36. Using the highest power of each prime makes 36 the smallest number both 12 and 18 divide into.
Use the distributive property to fully factor out the GCF of 36 + 48.
💡 Hint
Use the GREATEST common factor of 36 and 48 — what is left in the parentheses after dividing each by it?
GCF(36, 48) = 12. Then 36 ÷ 12 = 3 and 48 ÷ 12 = 4, so 36 + 48 = 12 × (3 + 4) = 12 × 7 = 84. ✓ (Choice B uses 6, which is not the greatest common factor.) Pulling out the full GCF leaves co-prime numbers (3 and 4) inside, the sign you've factored completely.
7.2 ÷ 0.09 = ?
💡 Hint
How many places must you slide both numbers to make 0.09 a whole number?
Multiply both by 100 to clear the decimals: 720 ÷ 9 = 80. 0.09 has two decimal places, so both numbers shift two places and the ratio stays the same.
Grounded in CA CCSS-M, Grade 6 · 6.NS, California Department of Education. Image generated with Gemini Nano Banana Pro.
