# 3rd Grade - Fractions And Decimals Are Equal

 Grade Level: 3rd Skill: Fractions and Probability Topic: Fractions and Decimals Are Equal Goal: Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1 - 2 of a dollar, 75 cents is 3 - 4 of a dollar). Skill Description: Number Sense: understand fractions and decimals can be equal The ability to understand that fractions and decimals can be used as different representations of the same amount.

### Sample Problems

 (1) The word decimal comes from the Greek word, deka, meaning ten. The American system of money is based on decimals or multiples of ten. Our number places in counting are also based on multiples of ten. (2) Whole numbers get larger as they move to the left of the decimal point and fractions get smaller as they move to the right of the decimal point. When we write 1/10, we are writing a fraction. It becomes a decimal when we drop the denominator and change the fraction line to a decimal point as .1 5/10=.5, 7/10=.7, 12/100=.12, 25/100=.25 (3) 1/10 means 1 divided by 10. If we extend the dividend by using a decimal point, we can get the extra number places that we need to divide 1 by 10. 10 divided by 1.0. We have to show the quotient as a fraction, a decimal fraction, so we must put the decimal point right above the one in the dividend and the answer becomes 0.1. (4) We divide the numerator by the denominator each time we change a fraction to a decimal.

### Learning Tips

 (1) Use the fraction strip tenths (in the place value mat PDF) to begin to understand the relationship between fractions and decimals. Show children how to write each tenth as both a fraction and a decimal. Use the place value mat and write decimals ones, tenths, hundredths, thousandths on the mat. Make sure the decimal point is prominent between the ones and tenths. Repeat the place value activities using decimals instead. Have children represent each fraction tenth in decimals on the place value mat. Do this in words and numerals (e.g., seven tenths and 7/10). (2) Use a grid paper with 100 squares to represent hundredths. Have children color particular numbers of the square to understand the fractional parts to 1 whole. For example, color 20 squares for 1/5. (3) Use money to explore fractional equivalents. A parent can ask the child to show them half a dollar and the child can set out coins that equal fifty cents. (4) Have the child practice ordering from least to greatest. For example: 4.4, 4.7, 4.1 (4.1, 4.4, 4.7) (5) Use the attached decimal-fraction graphics to compare decimal-wedges and fractional-wedges. Use the blank ones to allow your child to practice writing the fraction 1/10 and the decimal .1 (or .10).

### Online Resources

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### Extra Help Problems

 (1) 1/2 = 1.0 divided by 2 = (0.5) (2) 1/5 = 1.0 divided by 5 = (0.2) (3) ¼ = 1.00 divided by 4 = (0.25) (4) 1/25 = 1.00 divided by 25 = (0.04) (5) 2/5 = 2.0 divided by 5 = (0.4) (6) 3/5 = 3.0 divided by 5 = (0.6) (7) 3/20= 3.00 divided by 20 = (0.15) (8) 9/20 = 9.00 divided by 20 = (0.45) (9) Reduce to decimals: ¾ (.75) (10) 6/10 (0.6) (11) 7/10 (0.7) (12) 4/5 (0.8) (13) 3/25 (0.12) (14) 6/25 (.24) (15) 8/20 (0.4) (16) 3/8 (.375) (17) 2/3 (.6666) (18) Memorize the following fraction to decimal conversion: 1 whole = 1.00 (19) ½ =.50 (20) 1/3=.33 1/3 (21) ¼=.25 (22) 1/5 = .20 (23) 1/6 = .16 2/3 (24) 1/7 = .14 2/7 (25) 1/8 = .125 (26) 1/9 = .11 1/9 (27) 1/10 = .10 (28) 1/11 = .09 1/11 (29) 1/12 = .08 1/3 (30) 2/3 = .66 2/3 (31) ¾ = .75