Problem 369 - Prealgebra

Question

Divide. Then check by multiplying. $$\frac{35}{7}$$

Step-by-Step Solution

Answer

The result is 5. Verification: \ \( 5 \times 7 = 35\).

Step 1: Understand the Division

The exercise is asking to divide 35 by 7, which can be written as \ \ \(\frac{35}{7}\).

Step 2: Perform the Division

Divide 35 by 7. To do this, find how many times 7 goes into 35 which is 5 times. Therefore, \ \( \frac{35}{7} = 5\).

Step 3: Verify the Result by Multiplying

To check the result, multiply the quotient (5) by the divisor (7). \ \ \( 5 \times 7 = 35 \). Since the product is equal to the original dividend (35), the division is verified.

Key Concepts

Division Verification

When we perform a division, it's important to ensure our answer is correct. This is where division verification comes in handy.
After dividing, we verify by multiplying our answer (quotient) by the divisor. If the result (product) matches the original number (dividend), we know our division is correct.
For example, we divided 35 by 7 and got 5. To check, we multiplied 5 (quotient) by 7 (divisor) and got 35, which matches our original number.
This confirms our division was accurate.

Basic Multiplication

Multiplication is a fundamental math operation that helps in verifying division results.
In our case, to verify \( \frac{35}{7} = 5 \), we multiplied 5 (quotient) by 7 (divisor).
Remember, multiplication is about finding the total of equal-sized groups. Here, we had 5 groups of 7 and calculated:
\( 5 \times 7 = 35 \).
This multiplication confirmed our division was correct because the product equaled the original number.

Quotient

The quotient is the result we get from a division problem.
In our division of 35 by 7, the quotient is 5. This means 7 fits into 35 exactly 5 times.
It's crucial to understand that the quotient represents how many times the divisor can be subtracted from the dividend before reaching zero.
If our quotient, when multiplied by the divisor, returns us to the dividend, then our division is correct. In our example: \( 5 \times 7 = 35 \) confirming that the quotient, 5, is correct.