Fractions, Decimals and Percentages Quiz — Secondary 1

Answer: 3/4

A fraction is in lowest terms when the numerator and the denominator have no common factor left except 1. Look for the greatest common divisor of 18 and 24. The divisors of 18 are 1, 2, 3, 6, 9, 18; the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest one they share is 6. Divide both parts by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4. Watch out: 9/12 and 6/8 are equal to 3/4, but they are not in lowest terms because 9 and 12 still share the factor 3, and 6 and 8 still share the factor 2.

Answer: 0.375

The fraction bar means "divided by", so 3/8 = 3 ÷ 8. Do the long division: 8 does not go into 3, so write 0 and a decimal point. 30 ÷ 8 = 3 remainder 6, so the first decimal is 3. Bring down a zero: 60 ÷ 8 = 7 remainder 4, so the second decimal is 7. Bring down a zero: 40 ÷ 8 = 5 remainder 0, so the third decimal is 5 and the division stops. Answer: 0.375. A useful check: 1/8 = 0.125, and 3 × 0.125 = 0.375.

Answer: 0.7

To compare numbers written in different notations, put them all in the same notation. Decimals are the easiest here. 0.7 stays 0.7. For 2/3, divide 2 by 3: 0.6666… For 68%, "percent" means "out of 100", so 68% = 68 ÷ 100 = 0.68. And 0.695 stays 0.695. Now line them up with the same number of decimals: 0.700, 0.667, 0.680, 0.695. The biggest is 0.700, so 0.7 wins. The trap is 0.695, which looks long and therefore big — but the number of digits has nothing to do with the size.

Answer: 11/15

You can only add fractions that share the same denominator, because the denominator says what size the pieces are. The denominators are 5 and 3, so use their least common multiple: 15. Rewrite each fraction with 15 underneath. For 2/5, multiply top and bottom by 3: 2/5 = 6/15. For 1/3, multiply top and bottom by 5: 1/3 = 5/15. Now add the numerators only: 6/15 + 5/15 = 11/15. Since 11 is prime and does not divide 15, the answer is already in lowest terms. The classic mistake is 3/8 — adding the tops and the bottoms separately, which is never how fractions add.

Answer: 100

"Percent of" means multiply by the percentage written as a decimal. First turn 40% into a decimal by dividing by 100: 40% = 0.40. Then multiply: 0.40 × 250 = 100. If you prefer mental math, 10% of 250 is 25 (just move the decimal point one place left), and 40% is four times that: 4 × 25 = 100. Both roads give the same answer: 100.

Answer: 7/12

You can only add or subtract fractions that share the same denominator, because the denominator says how big the pieces are. The denominators are 6 and 4, so use their least common multiple. The multiples of 6 are 6, 12, 18; the multiples of 4 are 4, 8, 12 — the smallest they share is 12. Rewrite both fractions over 12. For 5/6, multiply top and bottom by 2: 5/6 = 10/12. For 1/4, multiply top and bottom by 3: 1/4 = 3/12. Now subtract the numerators only: 10/12 − 3/12 = 7/12. Since 7 is prime and does not divide 12, that is already in lowest terms. Each wrong option comes from a specific slip. The answer 4/2 subtracts the tops and the bottoms separately, which is never how fractions work. The answer 13/12 adds instead of subtracting. And 4/24 comes from multiplying the denominators to get 24 instead of using the least common multiple, then subtracting the original numerators without converting them. A sanity check catches all three: 5/6 is a bit more than 0.83 and 1/4 is 0.25, so the answer should sit near 0.58, and 7/12 = 0.583.

Answer: 60

There are two ways, and both must agree. First way: calculate the discount, then subtract it. 25% of 80 is 0.25 × 80 = 20, so you save $20 and pay 80 − 20 = $60. Second way, faster: if you get 25% off, you still pay 100% − 25% = 75% of the price. So the sale price is 0.75 × 80 = $60. The second method is worth learning, because it is one single multiplication instead of two steps — and it is the one you will reuse for successive discounts.

Answer: 6/25

Read the decimal out loud: 0.24 is twenty-four hundredths, because the last digit sits in the hundredths place. That gives 24/100 straight away. Now reduce. The greatest common divisor of 24 and 100 is 4: 24 ÷ 4 = 6 and 100 ÷ 4 = 25, so 0.24 = 6/25. Check that 6 and 25 share nothing: 6 = 2 × 3 and 25 = 5 × 5, no common factor, so we are done. The answers 24/100 and 12/50 have the right value but are not in lowest terms, and the question asked for the reduced form. As for 1/4, it is tempting because 1/4 = 0.25 sits very close to 0.24 — but close is not equal, and a fraction has to give back exactly the decimal you started from.

Answer: 60 %

A percentage is a part compared to the whole, written out of 100. Start by writing the part over the whole as a fraction: 15 girls out of 25 students is 15/25. Now turn that fraction into a percentage. The clean route here is to notice that 25 goes into 100 exactly four times, so multiply top and bottom by 4: 15/25 = 60/100 = 60%. The general route works too: divide, then multiply by 100. 15 ÷ 25 = 0.6, and 0.6 × 100 = 60%. Check the answer against common sense: 15 is more than half of 25, so the percentage must be above 50, and 60 is. Note also what the remaining part tells you — 10 boys out of 25 is 40%, and 60% + 40% = 100%, the whole class.

Answer: 62.5 %

Start by counting. The bar is cut into 8 equal parts and 5 of them are shaded, so the shaded portion is the fraction 5/8. Now convert that fraction into a percentage. Divide first: 5 ÷ 8 = 0.625. Then multiply by 100: 0.625 × 100 = 62.5%. So a little under two thirds of the bar is shaded. A second route avoids the division: 1/8 of a whole is 100% ÷ 8 = 12.5%, and five eighths is 5 × 12.5% = 62.5%. Both give 62.5.

Answer: 30 minutes

In a problem, the word "of" between a fraction and a quantity means multiply. So you need 2/3 × 45. The clean way is to do the denominator first: one third of 45 is 45 ÷ 3 = 15 minutes. Two thirds is twice as much: 2 × 15 = 30 minutes. As a check, the remaining third is 15 minutes, and 30 + 15 = 45, the whole period. The answer 15 minutes is the trap — that is only one third. And 67.5 would be 3/2 of the period, which is longer than the class itself, so it cannot be right.

Answer: 7.2

Written as a decimal, 15% is 0.15, so the tip is 0.15 × 48 = 7.20 dollars. The mental method restaurants everywhere use is worth knowing: 10% of 48 is 4.80 (move the decimal point one place left), half of that is 5%, so 2.40, and 10% + 5% = 15% gives 4.80 + 2.40 = 7.20. Same answer, no calculator. The total bill would then be 48 + 7.20 = 55.20 dollars.