Multiply and simplify. [tex]$\frac{7}{9} \cdot \frac{3}{5}$[/tex]
Answer (1)
Multiply the numerators and denominators: 9 7 ⋅ 5 3 = 9 × 5 7 × 3 = 45 21 .
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 45 ÷ 3 21 ÷ 3 = 15 7 .
The simplified fraction is 15 7 .
Explanation
Understanding the Problem We are given the expression 9 7 ⋅ 5 3 to multiply and simplify. Our goal is to find the product of these two fractions and reduce it to its simplest form.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 9 7 ⋅ 5 3 = 9 × 5 7 × 3 = 45 21
Simplifying the Fraction Now we need to simplify the fraction 45 21 . We look for common factors between the numerator and the denominator. Both 21 and 45 are divisible by 3. So, we divide both the numerator and the denominator by 3: 45 21 = 45 ÷ 3 21 ÷ 3 = 15 7
Final Answer The fraction 15 7 is now in its simplest form because 7 and 15 have no common factors other than 1. Therefore, the simplified product of the given fractions is 15 7 .
Examples
In baking, you might need to adjust a recipe that calls for 9 7 of a cup of flour, but you only want to make 5 3 of the recipe. Multiplying these fractions, as we did, tells you exactly how much flour you need: 15 7 of a cup. This kind of calculation is essential for scaling recipes up or down to get the right proportions.
