Ratios with Fractions.

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Presentation transcript:

Ratios with Fractions

Ratios with Fractions You can have a ratio where one term is a fraction. Simplify these ratios by finding an equivalent ratio where both terms are whole numbers. Multiply each term of the ratio by the denominator of the fraction. Then write the ratio in simplest form.

Ratios with Fractions The ratio (4/5)/6 written in simplest form is 2/15 .

Ratios with Fractions Your neighbor commutes 12 miles to work. You commute 9/10 miles to school. Write the ratio of your neighbor’s commute to your commute as a fraction in simplest form.

Ratios with Fractions Your neighbor commutes 12 miles to work. You commute 9 10 miles to school. Write the ratio of your commute to your neighbor’s commute as a fraction in simplest form.

Ratios with Fractions Your neighbor commutes 12 miles to work. You commute 9 10 miles to school. How are the ratios from each part related? The ratios 40/3 and 3/40 are reciprocals.

Ratios with Fractions An athlete runs on a treadmill for 3/4 hours. The athlete then lifts weights for 2 hours. Write the ratio of the running time to the weight-lifting time as a fraction in simplest form.

Ratios with Fractions You can also have ratios where both terms are fractions. Simplify these ratios by finding an equivalent ratio by finding an equivalent ratio where both terms are whole numbers. Multiply each term of the ratio by the least common multiple (LCM) of the denominators of the fractions. Then write the ratio in simplest form.

Ratios with Fractions The ratio (3/4)/(6/7) written in simplest form is 7/8 .

24 21 Ratios with Fractions Simple Method: Outside over Inside 3 ÷ __ ___ 3 4 6 7 24 21 ÷ = __ 8

Ratios with Fractions ___ Determine whether each statement is true or false. The ratio is equivalent to 10/3 . The ratio is equivalent to 14/15 . __ 2 3 ft² 1 5 ___ 4 6 7

Ratios with Fractions Write the ratio in simplest form. ___ __ 3 gal 4 9 10 ___ Write the ratio in simplest form.

Ratios with Fractions A professional football field is 53 1/3 yards wide. Find the ratio of the width of the actual field to the width of the field in the poster as a fraction in simplest form.

Ratios with Fractions = A professional football field is 53 1/3 yards wide. First, convert yards to feet. 53 yards = 160/3 × = 160 ft Then find the ratio of the width of the actual field to the width of the field in the poster as a fraction in simplest form. __ 1 3 3 ft 1 yd ___ 2 ft 160 ft =

Ratios with Fractions A square garden has a side length 5 3/4 yds. A square flower bed measures 7 2/3 yds on each side. (First, change yards to feet.) What is the ratio of the side length of the garden to the side length of the flower bed in simplest form? What is the ratio of the area of the garden to the area of the flower bed?

HW: Complete the Ratios with Fractions Worksheet.