Grade 5 · Subtract sixths from fourths · 47 of 750
Subtract sixths from fourths: numerator of the fourths: 10; numerator of the sixths removed: 2
A measured supply at a classroom activity combines 10/4 of a unit with the removal of 2/6 of the same unit. Find the exact difference in a common fractional unit, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A measured supply at a classroom activity combines 10/4 of a unit with the removal of 2/6 of the same unit. First find the exact difference in a common fractional unit. Then answer: What exact amount remains after the stated combination? Explain the common unit.
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A starting point
Fractions can be combined by counting a common fractional unit. Equivalent renaming changes the denominator and numerator together, allowing the signed counts to be added or subtracted without changing the original amounts.
Work through the reasoning
Step 1
Identify the quantities and the task
A measured supply at a classroom activity combines 10/4 of a unit with the removal of 2/6 of the same unit. The first task is to find the exact difference in a common fractional unit. Fractions can be combined by counting a common fractional unit. Equivalent renaming changes the denominator and numerator together, allowing the signed counts to be added or subtracted without changing the original amounts.
Step 2
Calculate the original result
10/4 − 2/6 = 26/12. Rename the amounts as 30/12 and 4/12. The result simplifies to 13/6.
Step 3
Complete the follow-up calculation
What exact amount remains after the stated combination? Explain the common unit. 26/12 = 13/6 units. Both terms are counted in 12ths before the subtraction.
The answer
10/4 − 2/6 = 26/12. Rename the amounts as 30/12 and 4/12. The result simplifies to 13/6. Follow-up: 26/12 = 13/6 units. Both terms are counted in 12ths before the subtraction.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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The mathematical idea
A measured supply at a classroom activity combines 10/4 of a unit with the removal of 2/6 of the same unit. Fractions can be combined by counting a common fractional unit. Equivalent renaming changes the denominator and numerator together, allowing the signed counts to be added or subtracted without changing the original amounts. Rename the amounts as 30/12 and 4/12. The result simplifies to 13/6.
10/4 − 2/6 = 26/12
03 · Reflect and transfer
Explain what changes and why.
Compare the original amounts on a common scale, then track the second contribution joining or leaving the first amount. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.