Fractions Test
Answer all 15 questions to test your understanding. Your results will be shown at the end.
A measuring cup contains 1/2 cup of juice. Someone adds another 1/4 cup, and you want to express both amounts in fourths before adding.
Which calculation changes the way the original amount is written without changing its value?
A team is designing a visual explanation of 1/2 + 1/4 = 3/4. Each proposed model uses identical whole-sized strips unless its description says otherwise.
Which models correctly demonstrate the addition? Select all that apply.
- Divide a strip into four equal parts; shade two parts for 1/2 and one additional part for 1/4.
- Divide a strip into six equal parts; shade one part for each numerator to represent a total of 2/6.
- Place a half-strip and a quarter-strip end to end; compare their combined length with a whole strip.
- Divide each half of a strip into two equal pieces; count two pieces from the half and one more quarter-piece.
Two identical pizzas are available. A learner combines half of one pizza with a quarter of the other and describes the total in units of one pizza.
Assertion: The combined amount is 3/4 of one pizza. Reason: Because the pizzas are the same size, the half-pizza can be represented as two quarter-pizza pieces and combined with one more quarter-pizza piece.
A recipe uses 1/2 cup of milk initially and another 3/4 cup later. Four colleagues calculate the total amount of milk.
Which calculation preserves both amounts and gives the correct total?
A container holds 5/2 liters of water, and another 3/4 liter is poured in. Record the total as a single fraction with denominator 4.
The total amount of water is ___ liters.
Four containers hold 1/2, 1/2, 3/2, and 3/2 liters respectively. The added amounts are 1/4, 3/4, 1/4, and 3/4 liter respectively.
Match each container's addition to its total amount.
A batch uses 2/3 kilogram of flour, and you are making 3/4 of the batch. Two colleagues disagree about whether the fractions need a common denominator before calculating 2/3 × 3/4.
Which calculations correctly find the required flour? Select all that apply.
- (2 × 3)/(3 + 4) = 6/7 kilogram.
- (2 × 3)/(3 × 4) = 6/12 = 1/2 kilogram.
- (8 × 9)/12 = 72/12 = 6 kilograms, after rewriting both fractions in twelfths.
- (8 × 9)/(12 × 12) = 72/144 = 1/2 kilogram, after rewriting both fractions in twelfths.
A bottle contains 3/4 liter of concentrate. You use 2/3 of the bottle's contents, so the amount used is represented by 3/4 × 2/3.
Which amount was used?
A calculation template for 2/3 × 3/4 requires three lines: first show the numerator and denominator multiplications, then evaluate those products, and finally simplify. The three completed lines have been shuffled.
Arrange the lines to complete the template in the required order.
A dispenser contains 2/3 liter of liquid. Each serving is 1/4 liter, and partial servings are allowed when calculating how many servings the dispenser contains.
Assertion: The number of servings is 2/3 ÷ 1/4 = 1/6. Reason: Dividing by 1/4 can be calculated by multiplying by 4/1.
A 3/4-meter ribbon is measured in units of 1/2 meter. A spreadsheet must calculate 3/4 ÷ 1/2, and its output may be an expression, an improper fraction, or a mixed number.
Which spreadsheet outputs correctly represent the result? Select all that apply.
- 3/4 × 2/1
- 6/4
- 1 1/2
- 3/8
A machine processes 4/5 kilogram per full cycle. You have 2/3 kilogram to process and need the fraction of a cycle required.
Written as a fraction in lowest terms, 2/3 ÷ 4/5 = ___.
An answer sheet contains four lines: A gives 2/3 × 3/5 = 6/3; B gives 3/4 ÷ 2/5 = 6/20; C gives 2/7 ÷ 3/4 = 7/2 × 3/4 = 21/8; D gives 3/5 × 2/7 = 5/12. Each line needs a correction.
Match each line to the correction that fixes its rule misuse.
A reviewer checks four results: A, 1/2 × 2/3 = 2/6 = 1/3; B, 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8; C, 2/5 × 3/4 = 6/9; and D, 5/6 ÷ 1/2 = 5/6 × 2/1 = 10/6 = 5/3.
Which audit correctly identifies all lines needing correction?
Four worked results are under review: A, 2/3 × 3/4 = 6/12; B, 4/5 ÷ 2/3 = 8/15; C, 3/7 × 2/5 = 5/12; and D, 1/2 ÷ 3/4 = 2/3. Reviewers propose the following changes.
Which proposed changes repair an actual error and give the correct result? Select all that apply.
- Change A to 72/12 = 6 after converting both factors to twelfths.
- Change B to 4/5 × 3/2 = 12/10 = 6/5.
- Change C to (3 × 2)/(7 × 5) = 6/35.
- Change D to 1/2 × 3/4 = 3/8.