Problem
The whole is one; find the remaining fraction
Sea spends of her money on snacks, then spends of what is left on school supplies. Write, as a fraction of the money she started with, how much is left.
Fractions
Your answer
Watch out It's tempting to take of the original whole, but the problem says comes out of what was left after snacks (), not the starting amount.
How to solve
Strategy Identify Subproblems — Solve it in stages: first the money left after snacks (whole minus ), then the fraction of that remainder still left after spending of it. A bar model makes the 'fraction of what is left' step clear.
1STEP 1
Money left after snacks
The whole is 1 = . Spending leaves - = of the original money.
Since the whole is 1, what is left is simply 1 minus the part spent.
3.NF.A.3Identify Subproblems2STEP 2
Fraction of the remainder still left
She spends of what was left, so - = of the remainder stays. The applies to the she had after snacks.
Spending 2 of every 7 equal parts of the remainder leaves 5 of those 7 parts.
3.NF.A.1Draw A Diagram3STEP 3
Combine to a fraction of the whole
Take of . Split the into 7 equal parts of each; 5 of them are left, which is of the original money.
Seven twelfths split into 7 equal pieces gives pieces of , and keeping 5 of them is .
3.NF.A.1Identify SubproblemsTaking of the that is left lands on a whole number of twelfth-sized pieces, so it is again a plain fraction of the money she started with.
Why?
The left after snacks is just seven equal pieces, each one of the whole.
Why?
A twelfth comes from cutting the whole into 12 equal pieces with nothing left over, and simply collects seven of those single pieces.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Taking of a batch of seven equal pieces keeps exactly five of the pieces, a whole count.
Why?
The seven equal shares that sevenths cut the batch into match the seven pieces one for one, so each share is one piece and five shares are five pieces.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Five kept pieces, each of the whole, together make five twelfths of the whole.
Why?
Five copies of is added over and over five times, which counts up to that many twelfths.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Answer
of = (5 × 7)/(7 × 12) =
After snacks remains; she then spends a bit more, so the final amount must be less than . The answer is less than and still positive, which fits. Check: spent on snacks plus on supplies ( of ) = spent, leaving .
Takeaway
The whole is just 1, so subtract each part spent in turn to find the fraction that is left!
- Money left after snacks
- Fraction of the remainder still left
- Combine to a fraction of the whole
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested