Problem 84 Divide. Write the quotient as a ... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 84

Divide. Write the quotient as a mixed number. $$695 \div 34$$

Short Answer

Expert verified

20 \frac{15}{34}

Step by step solution

Set up the division

Write the division of 695 divided by 34 as a division problem: \[ 695 \div 34 \]

Perform the division

Divide 695 by 34. The quotient is 20 with a remainder. \[ 695 \div 34 = 20 \text{ R } 15 \]

Express the remainder as a fraction

Take the remainder (15) and write it as a fraction with the divisor (34) as the denominator. \[ \text{Remainder as a Fraction} = \frac{15}{34} \]

Write the quotient as a mixed number

Combine the quotient from step 2 and the fractional remainder from step 3 to form the mixed number. \[ 20 \frac{15}{34} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

mixed numbers

A mixed number is a combination of a whole number and a fraction. It's helpful when expressing division results that don't divide evenly. In our example, $695 \div 34$, the quotient is 20 with a remainder. To convert this into a mixed number, you combine the whole number quotient and the fractional part of the remainder over the divisor. Therefore, we arrive at $20 \frac{15}{34}$. This way, you can neatly represent the division result where part of it is a fraction.

remainder

The remainder is what is left over after performing a division. It represents the part of the dividend that isn't fully divisible by the divisor. In our example of $695 \div 34$, when you divide 695 by 34, you get a quotient of 20, but there are 15 left over (695 - 680 = 15). This 15 is our remainder. When representing the division result as a mixed number, this remainder is crucial as it turns into the fractional part of the mixed number: 20 \frac{15}{34}.

long division

Long division is a method used to divide large numbers. It breaks down a division problem into simpler steps, making it manageable. Here's how you can perform it with the example of $695 \div 34$:
- Write 695 inside the division bracket and 34 outside.
- Determine how many times 34 goes into 69 (which is 2). Place the 2 above the bracket.
- Multiply 34 by 2, getting 68, and subtract it from 69, resulting in 1.
- Bring down the next digit (5) to make it 15.
- Determine how many times 34 goes into 15 (which is 0).
- Hence, the quotient is 20, and the remainder is 15.
Converting this into a mixed number will give you 20 \frac{15}{34}.

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91影视

Divide. Write the quotient as a mixed number. $$695 \div 34$$

Short Answer

Step by step solution

Set up the division

Perform the division

Express the remainder as a fraction

Write the quotient as a mixed number

Key Concepts

mixed numbers

remainder

long division

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