Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Compare Rational Numbers Example 2:Compare Rational Numbers Example 3:Real-World Example Example 4:Real-World Example Key Concept:Fraction-Decimal Equivalents Five-Minute Check

Main Idea/Vocabulary Compare and order fractions and decimals. rational numbers common denominator least common denominator (LCD)

NGSSS MA.7.A.5.1 Express rational numbers as terminating or repeating decimals.

Example 1 Compare Rational Numbers Replace the O with, or = to make O a true sentence. Graph each rational number on a number line. Mark off equal-size increments of between –4 and –3. __ 1 8 Answer: The number line shows that

Example 1 CYP A.< B.> C.= Replace the O with, or = to make O a true sentence.

Example 2 Compare Rational Numbers The LCD of the denominators 4 and 5 is 20. Answer: Replace the O with, or = to make O a true sentence.

Example 2 CYP A.< B.> C.= Replace the O with, or = to make O a true sentence.

Example 3 FOOTBALL In a game against Virginia Tech, Florida State Seminoles quarterback Christian Ponder completed 11 out of 19 passes. The next week against Georgia Tech, he completed 16 out of 27 passes. Against which team did he complete the greater fraction of his passes? Since the denominators are large, write and as decimals and then compare. Answer: He completed a greater fraction of his passes against Georgia Tech. 11 ÷ 19 ≈ ÷ 27 ≈ Divide.

Example 3 CYP A.Mrs. Park’s class B.Mr. Randazzo’s class C.The fraction is the same for both classes. PENCILS In Mrs. Park’s math class, 5 out of 31 students are using mechanical pencils. In Mr. Randazzo’s class 3 out of 27 students are using mechanical pencils. In which class are a greater fraction of students using mechanical pencils?

Example 4 Line up the decimal points and compare using place value. List the numbersin order from least to greatest. 0.70= 0.7 Annex a 0. __ =

Example Annex a = 0.64 __ Answer: So, the order of the numbers is

Example 4 Check Graph each number on a number line. The number line confirms the order of the numbers is correct.

Example 4 CYP A. B. C. D. List the numbers in order from least to greatest.

Key Concept 5

A.< B.> C.= Five Minute Check 1 Replace the O with, or = to make O a true statement. Use a number line if necessary.

A.< B.> C.= Five Minute Check 2 Replace the O with, or = to make O a true statement. Use a number line if necessary.

A.< B.> C.= Five Minute Check 3 Replace the O with, or = to make O a true statement. Use a number line if necessary.

A.< B.> C.= Five Minute Check 4 Replace the O with, or = to make O a true statement. Use a number line if necessary.

Five Minute Check 5 Order 0.75,, and 65% from least to greatest. A., 0.75, 65% B.65%,, 0.75 C.65%, 0.75, D., 65%, 0.75

Five Minute Check 6 Order –3.55, –3.46, and from least to greatest. A.–3.55,, –3.46 B.–3.55, –3.46, C., –3.55, –3.46, D.–3.46, –3.55,

A.litter 1 B.litter 2 C.The ratios are equal. D.not enough information to determine In one litter of kittens, 2 out of 5 were male. In a second litter, 4 out of 6 were male. Which litter had the greater percentage of male kittens? Five Minute Check 7