Understanding Fraction and Decimal Equivalence in Math
Discover how to express fractions with denominators of 10 as equivalent fractions with denominators of 100 in order to add them together. Learn to use decimal notation for fractions and explore essential questions on equivalent fractions, decimal conversion, and converting decimals to fractions. Engage in hands-on activities to reinforce the concepts.
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Lesson 21 Fraction and Decimal Equivalence
[OBJECTIVE] The student will be able to express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators 10 and 100. The student will be able to use decimal notation for fractions with denominators of 10 and 100.
[MYSKILLS] Basic understanding of a fraction Understanding of place value
[ESSENTIALQUESTIONS] 1. What are equivalent fractions? 2. How do you change a fraction to a decimal when the denominator is 10 or 100? 3. How do you change a decimal in the tenths or hundredths place to a fraction?
[LESSON] For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. S Study the Problem Underline the question. This problem is asking me to find the entire distance the ball rolled in both trials given in decimal form. 2 __ 10 62 ___ 100
[Cooperative Pairs] Partner A Partner B
Equivalent Fractions How many sections are in each grid? 10 sections Tenths 100 sections Hundredths When each picture is completely shaded, it represents one whole.
Equivalent Fractions Represent the fraction by creating 3 groups of 10. by the centimeter cubes? 3 3 __ 10 How many vertical strips are covered 3 10
Equivalent Fractions Now, slide the three strips of ten over to the hundredths chart.
Equivalent Fractions There are 30 squares covered in the hundredths chart Did the number of centimeter cubes change when we slid them to the next chart? NO
Equivalent Fractions What fraction can we write to represent the hundredths chart? 30 100
Equivalent Fractions What can we conclude about the two fractions we created? They are EQUIVALENT FRACTIONS! 3 10 30 100 =
Equivalent Fractions How many bars do we need to shade in the tenths grid? Fraction TENTHS 3 10
Equivalent Fractions How many squares do we need to shade in the hundredths grid? TENTHS HUNDREDTHS
Equivalent Fractions Write the equivalent fractions EQUIVALENT FRACTIONS HUNDREDTHS 3 30 100 = 10
Equivalent Fractions How many bars do we need to shade in the tenths grid? Fraction TENTHS 7 10
Equivalent Fractions How many squares do we need to shade in the hundredths grid? TENTHS HUNDREDTHS
Equivalent Fractions Write the equivalent fractions EQUIVALENT FRACTIONS HUNDREDTHS 7 70 100 = 10
Equivalent Fractions How many bars do we need to shade in the tenths grid? First Fraction Fraction 4 32 100 + 10
Equivalent Fractions How many squares do we need to shade in the hundredths grid? Second Fraction Fraction 4 32 100 + 10
Equivalent Fractions Remember, we can t add fractions unless we have a common denominator. First Fraction Second Fraction +
Equivalent Fractions How did this example use a pictorial model to show equivalent fractions? Four tenths is the same as forty hundredths. TENTHS HUNDREDTHS
Equivalent Fractions Shade in the equivalent fractions on the hundredths grids below. First Fraction Second Fraction +
Equivalent Fractions First Fraction Second Fraction + +
Equivalent Fractions Shade both fractions on the SUM grid. First Fraction Second Fraction SUM + = 72 100
Equivalent Fractions 32 100 4 40 100 32 100 = + + 10 40 100 32 100 72 100 = +
Equivalent Fractions How many bars do we need to shade in the tenths grid? First Fraction Fraction 5 11 100 + 10
Equivalent Fractions How many squares do we need to shade in the hundredths grid? Second Fraction Fraction 5 11 100 + 10
Equivalent Fractions Remember, we can t add fractions unless we have a common denominator. First Fraction Second Fraction +
Equivalent Fractions How have we used a pictorial model to show equivalent fractions? hundredths grids. By shading the same area in the tenths and TENTHS HUNDREDTHS
Equivalent Fractions Shade in the equivalent fractions on the hundredths grids below. First Fraction Second Fraction +
Equivalent Fractions First Fraction Second Fraction + +
Equivalent Fractions Shade both fractions on the SUM grid. First Fraction Second Fraction SUM + = 61 100
Equivalent Fractions 11 100 5 50 100 11 100 = + + 10 50 100 11 100 61 100 = +
Tenths as Fractions and Decimals Another way to represent a fraction is as a DECIMAL Where have you seen decimals before?
Tenths as Fractions and Decimals What place values do you see to the right of the decimal point in our Place Value Chart? Hundredths Hundreds Tenths Ones Tens In Part I of our lesson, we used tenths and hundredths to add fractions on our grids!
Tenths as Fractions and Decimals Shade the fraction in the TENTHS grid. Fraction TENTHS 3 10
Tenths as Fractions and Decimals Write the fraction in words. Written Words TENTHS Three tenths
Tenths as Fractions and Decimals How many tenths do we have? What would the decimal be if we had four tenths? six tenths? What would the decimal be if we had Written Words Place Value Chart Hundredths Tenths Ones Tens Three tenths 0 3 4 6
Hundredths as Fractions and Decimals Shade the fraction in the HUNDREDTHS grid. Fraction HUNDREDTHS 32 100
Hundredths as Fractions and Decimals Write the fraction in words. Written Words HUNDREDTHS Thirty-two hundredths
Hundredths as Fractions and Decimals How many hundredths do we have? Thirty-two hundredths Written Words Place Value Chart Hundredths Tenths Ones Tens Thirty-two hundredths
Hundredths as Fractions and Decimals Let s break thirty-two hundredths down into tenths and hundredths. = + 3 Tenths 2 Hundredths
Hundredths as Fractions and Decimals How many tenths do we have? How many hundredths do we have? Written Words Place Value Chart Hundredths Tenths Ones Tens Three tenths 0 3 2
Fraction and Decimal Equivalence Identify what information is given and use this information to complete the chart. Fraction TENTHS 8 10 Given
Fraction and Decimal Equivalence Write the fraction in words. Written Words TENTHS Eight tenths
Fraction and Decimal Equivalence Write the fraction as a decimal. Written Words Place Value Chart Hundredths Tenths Ones Tens Eight tenths 0 8
SOLVE For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. S Study the Problem Underline the question. This problem is asking me to find the entire distance the ball rolled in both trials given in decimal form. 2 __ 10 62 ___ 100
For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. 2 __ 10 62 ___ 100 O Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. First trial = of a meter Second trial = of a meter 2 ___ 10 62 ___ 100
L Line Up a Plan Choose an operation or operations. Addition Write in words what your plan of action will be. Add the distance of the second trial to the distance of the first trial. Then, change the final fraction to a decimal.
