SBAC Math Grade 5 Fractions and Decimals 2 — Questions and Answers
Question 1: What is 3/4 + 2/3?
- 5/7
- 5/12
- 17/12 (Correct answer)
- 1/2
Correct answer: 17/12
To add fractions with unlike denominators, find the LCD (12), convert: 9/12 + 8/12 = 17/12.
To add fractions with different denominators, we must first find the least common denominator (LCD) — the smallest number that both denominators divide into evenly. For 3/4 + 2/3: the denominators are 4 and 3. The LCD of 4 and 3 is 12 (since 4 × 3 = 12, and there are no smaller common multiples). Convert 3/4: multiply numerator and denominator by 3 → 9/12 Convert 2/3: multiply numerator and denominator by 4 → 8/12 Now add: 9/12 + 8/12 = 17/12 17/12 is an improper fraction (numerator > denominator). As a mixed number: 17/12 = 1 and 5/12. Both 17/12 and 1 5/12 are correct ways to express the answer. Never add denominators when adding fractions — 3/4 + 2/3 ≠ 5/7. The denominators tell you the size of the pieces; you must use equal-sized pieces before combining.
Question 2: What is 0.6 × 0.4?
- 0.024
- 0.24 (Correct answer)
- 2.4
- 24
Correct answer: 0.24
0.6 × 0.4: multiply 6 × 4 = 24, then place the decimal point 2 places from the right (one decimal place in each factor = two total), giving 0.24.
To multiply decimals, use this process: (1) ignore the decimal points and multiply as if they were whole numbers, (2) count the total number of decimal places in both factors, (3) place the decimal point that many places from the right in the product. 0.6 has 1 decimal place; 0.4 has 1 decimal place. Total: 2 decimal places. 6 × 4 = 24 Place decimal 2 places from the right: 0.24 You can verify this makes sense using estimation. 0.6 is a bit more than 1/2, and 0.4 is a bit less than 1/2. Half of a half is 1/4 = 0.25. So 0.24 is a reasonable answer. Another way to understand it: 0.6 = 6/10 and 0.4 = 4/10. Multiplying fractions: (6/10) × (4/10) = 24/100 = 0.24. The denominator becomes 100 (10 × 10), which equals 2 decimal places — confirming the rule.
Question 3: What is 5/6 − 1/4?
- 4/2
- 7/12 (Correct answer)
- 4/12
- 11/12
Correct answer: 7/12
LCD of 6 and 4 is 12. Convert: 10/12 − 3/12 = 7/12.
To subtract fractions with different denominators, find the LCD of 6 and 4. Multiples of 6: 6, 12, 18... Multiples of 4: 4, 8, 12, 16... LCD = 12 Convert 5/6: multiply by 2/2 → 10/12 Convert 1/4: multiply by 3/3 → 3/12 Subtract: 10/12 − 3/12 = 7/12 7/12 is already in simplest form (7 and 12 share no common factors other than 1). Always check if your answer can be simplified by finding the GCF (greatest common factor) of the numerator and denominator. If GCF = 1, the fraction is already in simplest form. Also check that your answer makes sense. 5/6 is close to 1, and 1/4 is a small amount. 5/6 − 1/4 should be a fraction that's less than 5/6 but still substantial. 7/12 ≈ 0.583, while 5/6 ≈ 0.833 and 1/4 = 0.25. 0.833 − 0.25 = 0.583 = 7/12. ✓
Question 4: Which decimal is equivalent to 3/8?
- 0.38
- 0.35
- 0.375 (Correct answer)
- 0.3
Correct answer: 0.375
3/8 = 0.375. Divide 3 ÷ 8: 8 goes into 30 three times (0.3), remainder 6; 8 goes into 60 seven times (0.07), remainder 4; 8 goes into 40 five times (0.005). So 3/8 = 0.375.
To convert a fraction to a decimal, divide the numerator by the denominator. For 3/8, calculate 3 ÷ 8. 3 ÷ 8: 8 doesn't go into 3, so write 0. and continue with 30. 8 goes into 30 three times (8 × 3 = 24), remainder 6. 8 goes into 60 seven times (8 × 7 = 56), remainder 4. 8 goes into 40 five times (8 × 5 = 40), remainder 0. 3 ÷ 8 = 0.375 You can verify: 0.375 = 375/1000. Simplify 375/1000 by dividing by 125: 3/8. ✓ Some fractions convert to terminating decimals (they end) and some to repeating decimals (they go on forever with a pattern). Fractions where the denominator's only prime factors are 2 and/or 5 will always terminate. Since 8 = 2³, 3/8 terminates at 0.375. Fractions like 1/3 = 0.333... repeat because 3 has prime factors other than 2 and 5.
Question 5: A recipe uses 2 1/2 cups of flour. If you want to make 3 batches, how many cups of flour do you need?
- 5 cups
- 6 cups
- 7 cups
- 7 1/2 cups (Correct answer)
Correct answer: 7 1/2 cups
2 1/2 × 3 = 5/2 × 3 = 15/2 = 7 1/2 cups. Convert the mixed number to an improper fraction before multiplying.
To multiply a mixed number by a whole number, convert the mixed number to an improper fraction first. 2 1/2 as an improper fraction: (2 × 2) + 1 = 5, so 2 1/2 = 5/2 Multiply: 5/2 × 3 = 5/2 × 3/1 = 15/2 Convert back to a mixed number: 15 ÷ 2 = 7 remainder 1, so 15/2 = 7 1/2 You need 7 1/2 cups of flour. You can check with estimation: about 2.5 cups per batch × 3 batches ≈ 7.5 cups = 7 1/2 cups. ✓ Real-world cooking and baking often involve fraction multiplication. Whenever you scale a recipe up or down, you're multiplying fractions. This skill is practical and important. Always convert mixed numbers to improper fractions before multiplying or dividing.
Question 6: What is 4.25 ÷ 0.5?
- 0.85
- 2.125
- 8.5 (Correct answer)
- 0.212
Correct answer: 8.5
4.25 ÷ 0.5: multiply both by 2 to eliminate the decimal in the divisor: 8.5 ÷ 1 = 8.5.
To divide by a decimal, the standard method is to multiply both the dividend and divisor by the same power of 10 to make the divisor a whole number. 0.5 has one decimal place, so multiply both by 10: 4.25 × 10 = 42.5 0.5 × 10 = 5 Now calculate 42.5 ÷ 5 = 8.5 Alternatively, multiply by 2 (since 0.5 = 1/2, dividing by 1/2 is the same as multiplying by 2): 4.25 × 2 = 8.5 Estimate to check: 4.25 ÷ 0.5 means 'how many half-units are in 4.25 units?' Each whole unit contains 2 halves, so 4 units contain 8 halves, plus 0.25 = 1/2 of a half = 0.5 more halves. Total: 8.5 halves. ✓ When dividing decimals, the key insight is that dividing by 0.5 is the same as multiplying by 2. Understanding the relationship between the divisor and the operation simplifies many problems.
SBAC Math Grade 5 Fractions and Decimals 2
What is 3/4 + 2/3?