Patterns & Reasoning

Depth · one concept from first principles · step 2 of 4

Rebuild the dividend with multiplication and addition

A number was divided by 6.46.4 and the quotient taken only as far as its whole-number part, giving a quotient of 55 and a remainder of 1.21.2. If the same number is divided by 9.59.5 in the same way, what is the remainder?

Number system
Your answer
How to solve
Strategy Work Backwards — The second division cannot start until the number itself is known, and the first division holds it: quotient times divisor plus remainder rebuilds the number exactly.
1STEP 1

Rebuild the number

A division says the number is the divisor times the quotient plus what was left over.

6.4 × 5 = 32, 32 + 1.2 = 33.2
2STEP 2

Find the new quotient

Count how many whole 9.5s fit inside 33.2 without going over.

9.5 × 3 = 28.5, 9.5 × 4 = 38
3STEP 3

Take the remainder

What is left over is the number minus what the three whole divisors accounted for.

33.2 - 28.5 = 4.7
Answer
4.7
Rebuild the second division too: 9.5 × 3 + 4.7 = 33.2, the same number, and 4.7 is less than 9.5 as a remainder must be.
Takeaway

Quotient times divisor plus remainder gives the original number back.

  • Rebuild the number
  • Find the new quotient
  • Take the remainder
Where next?
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Product of two numbers equals GCF times LCMA denominator that cancels to 1 leaves a whole number
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