5-1 Estimate with Fractions and Mixed Numbers Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

1. 5.2x = = = Bellwork Divide. x t 4.1 x 15.1

1. 5.2x = = = Bellwork Divide. x = 24.6 x = x = x t 4.1 x 15.1

Problem of the Day Fill in the square using the numbers 5–13 so that all sums (rows, columns, and main diagonals) are the same

Learning Objective: to estimate sums and differences of fractions and mixed numbers.

Sometimes, when solving problems, you may not need an exact answer. To estimate sums and differences of fractions and mixed numbers, round each fraction to 0,, or 1. you can use a number line to help is closer to than to

You can also round fractions by comparing numerators with denominators. Benchmarks for Rounding Fractions Round to 0 if the numerator is much smaller than the denominator. Examples: Round to 1212 if the numerator is about half the denominator. Examples: Round to 1 if the numerator is nearly equal to the denominator. Examples: , , ,

Additional Example 1: Measurement Application A blue whale can grow to 33 m long, while 3535 the great white shark may be as long as 4 m Estimate how much longer the blue whale is than the great white shark – Round each mixed number. Subtract. The blue whale is about 29 m longer. = 29– Round to, round to, and round to 1. Helpful Hint

Check It Out: Example – Round each mixed number. Subtract. = 8 – A Cocker Spaniel may grow to weigh about 11 kilograms while the Chihuahua will not weigh more than 2 kilograms. Estimate how much more the Cocker Spaniel weighs than the Chihuahua The Cocker Spaniel weighs about 8 kg more. 1212

Estimate each sum or difference. Additional Example 2: Estimating Sums and Differences A – – = 7979 Round each fraction. Add B Round each mixed fraction. Subtract =

Estimate the sum. Additional Example 2: Estimating Sums and Differences Add C. – – Round each number = – –2 In the fraction -2, the numerator is close in value to the denominator. So round -2 to -2. Helpful Hint

Estimate each sum or difference. Check It Out: Example 2 A – – 0 = Round each fraction. Add B Round each mixed fraction. Subtract =

Estimate the sum. Check It Out: Example 2 Add C. – – Round each number = – –4

You can estimate products and quotients of mixed numbers by rounding to the nearest whole number. If the fraction in a mixed number is greater than or equal to, you can round the mixed number up to the next whole number. If the fraction is less than, you can round down to a whole number by dropping the fraction

Products and Quotients: Round to nearest whole number. Fractions > round up Fraction < drop the fraction

Additional Example 3A: Estimating Products and Quotients Estimate each product or quotient. 3 7 = 21. Multiply Round each mixed number to the nearest whole number.

Additional Example 3B: Estimating Products and Quotients Estimate each product or quotient. 14 ÷ 2 = 7. Divide ÷ Round each mixed number to the nearest whole number.

Check It Out: Example 3A Estimate each product or quotient. 8 3 = 24. Multiply Round each mixed number to the nearest whole number.

Check It Out: Example 3B Estimate each product or quotient. 12 ÷ 3 = 4. Divide ÷ Round each mixed number to the nearest whole number.

Lesson Quiz Estimate each sum or difference. 1. The new show arena being built in Franklin County is 150 feet long and 110 feet wide. Estimate the difference between the length and width – – ft Estimate each product or quotient ÷