Math Problem Statement

(5/9 + 5/6)(7/8 + 3/7)

Solution

To solve (59+56)(78+37)(\frac{5}{9} + \frac{5}{6})(\frac{7}{8} + \frac{3}{7}), follow these steps:

Step 1: Add the fractions inside each parenthesis.

First Parenthesis: 59+56\frac{5}{9} + \frac{5}{6}

To add these fractions, we need a common denominator. The least common denominator (LCD) of 9 and 6 is 18.

59=1018,56=1518\frac{5}{9} = \frac{10}{18}, \quad \frac{5}{6} = \frac{15}{18}

Now, add the fractions:

1018+1518=2518\frac{10}{18} + \frac{15}{18} = \frac{25}{18}

Second Parenthesis: 78+37\frac{7}{8} + \frac{3}{7}

The LCD of 8 and 7 is 56.

78=4956,37=2456\frac{7}{8} = \frac{49}{56}, \quad \frac{3}{7} = \frac{24}{56}

Now, add the fractions:

4956+2456=7356\frac{49}{56} + \frac{24}{56} = \frac{73}{56}

Step 2: Multiply the results of both parentheses.

(2518)×(7356)=25×7318×56=18251008\left(\frac{25}{18}\right) \times \left(\frac{73}{56}\right) = \frac{25 \times 73}{18 \times 56} = \frac{1825}{1008}

Step 3: Simplify the fraction (if possible).

The greatest common divisor (GCD) of 1825 and 1008 is 1, so the fraction cannot be simplified further.

Thus, the final result is:

18251008\frac{1825}{1008}

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:

  1. How can you simplify a fraction more easily?
  2. How do you find the least common denominator (LCD) of two fractions?
  3. What are some common ways to check the accuracy of a fraction multiplication?
  4. How do you handle mixed numbers in operations like this?
  5. Can this fraction be represented as a decimal or percentage?

Tip: Always check if the fractions can be simplified before performing multiplication—it can save time in calculations!

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition of Fractions
Multiplication of Fractions
Least Common Denominator (LCD)

Formulas

Addition of fractions: (a/b) + (c/d) = (ad + bc) / bd
Multiplication of fractions: (a/b) * (c/d) = ac / bd

Theorems

Greatest Common Divisor (GCD)

Suitable Grade Level

Grades 7-9