Fraction Equivalence
A student says 3/5 and 9/15 are not equivalent because the numbers are different. Is this reasoning correct? Explain.
Yes, correct. 3/5 × 3/3 = 9/15 → equivalent fractions. What you do to the bottom, you do to the top when finding equivalent fractions.
A student drinks 1/3 liter of water in the morning and 1/6 liter later. How much total? Show reasoning.
1/3 + 1/6 = 1/2
A student walks 2/5 mile each day for 3 days. Total distance?
3 × 2/5 = 6/5 = 1 1/5
A student says 0.4 is greater than 0.35 because 4 > 35. Is this correct? Explain.
Incorrect. 0.4 = 0.40, which is greater than 0.35
A student says:
1/4 + 1/4 = 2/8
What mistake did they make?
Added denominators incorrectly; should be 2/4 = 1/2
On a number line, 2/3 is between 1/2 and 3/4. Explain how you know without converting to decimals.
2/3 > 1/2 because thirds are larger pieces than halves when comparing same whole positions; also 2/3 is further right on number line.
A rope is 5/4 meters long. 3/4 meter is cut off. How much remains?
5/4 − 3/4 = 2/4 = 1/2
A recipe uses 3/4 cup of milk. You make it 3 times. How much milk total?
3 × 3/4 = 9/4 = 2 1/4
A runner runs 1.25 miles and then 0.75 miles. What total distance?
1.25 + 0.75 = 2.00
A student solves:
3/5 + 2/5 = 5/10
Explain the error and give the correct answer.
Denominator should stay 5 → correct answer: 5/5 = 1
A pan is cut into 8 equal pieces. Two students each eat 2 pieces. Another student eats 4 pieces. Who ate more, or did they eat the same? Justify.
They ate the same. (2/8 + 2/8 = 4/8, which equals 4/8)
Noah ran 2/3 mile and then another 3/6 mile. What total distance did he run? Simplify.
2/3 + 3/6 = 2/3 + 1/2 = 7/6 = 1 1/6
A machine produces 5 batches, each using 2/3 pound of material. Total used?
5 × 2/3 = 10/3 = 3 1/3
Which is greater: 0.508 or 0.58? Explain using place value.
0.58 is greater (5 tenths vs 5 tenths, but 8 hundredths > 0 hundredths)
A student says:
4 × 1/3 = 4/12
What misunderstanding is shown?
Multiplied denominator incorrectly; should be 4/3
Create two fractions equivalent to 4/6 with different denominators greater than 6. Explain your method.
Examples: 8/12, 12/18 (multiply numerator & denominator by same number)
A tank is filled to 5/6. Then 1/3 of the tank is used. How much remains? (Be careful—interpret correctly.)
5/6 − 1/3 = 5/6 − 2/6 = 3/6 = 1/2
Each box holds 4/5 pound. How much do 7 boxes hold? Express as a mixed number.
7 × 4/5 = 28/5 = 5 3/5
A tank holds 3.5 liters. After using 1.75 liters, how much remains?
3.5 − 1.75 = 1.75
A student compares 0.7 and 0.65 and says 0.65 is greater because 65 > 7. Explain the error.
Ignored place value; 0.70 > 0.65
Which is closer to 1: 5/6 or 7/8? Explain your reasoning using distance from 1.
7/8 is closer to 1 (only 1/8 away vs 1/6 away) when you draw it on a number line.
Emma baked a cake. She used 3/4 cup of sugar and then added another 2/8 cup. How much sugar total? Simplify and explain.
3/4 + 2/8 = 3/4 + 1/4 = 1
A runner trains for 6 days, running 3/8 mile each day. Is the total distance greater than 2 miles? Justify.
6 × 3/8 = 18/8 = 9/4 = 2 1/4 → Yes, greater than 2 miles
A student claims 0.6 + 0.35 = 0.95 because 6 + 35 = 95. Is this valid reasoning? Why or why not?
Incorrect reasoning, but answer is correct (0.95). Must align place values, not combine digits.
student solves:
5/6 − 1/3 = 4/3
Identify the mistake and explain the correct process.
Didn’t find common denominator correctly; answer is 1/2