Mathematics Class on Decimals

Converting Fractions to Decimals

• Write a proper fraction as a decimal fraction
  • 5/100

Place Value

• Write the place value of the digit 4 in the number 7.004
  • Thousandths

Standard Form

• Write the number > in standard form.
  • The exact number is required to answer this question.

Word Form

• Write the decimal fraction 0.54 in word form
  • Fifty-four hundredths

Comparing Decimals

• Ahmed says that the decimal fraction 0.740 is equal to the decimal fraction 0.74, Do you agree with him?
  • Yes, adding zeros to the right of a decimal fraction does not change its value.

Word Form (2)

• Write the number 65.75 in word form.
  • Sixty-five and seventy-five hundredths

Mass Calculations

• The mass of a box of apples is 18.75 kg. What is the mass of 10 boxes of the same type?
  • 18.75 x 10 = 187.5 kg

Expanded Form

• Write the number 75.654 in expanded form.
  • (7 x 10) + (5 x 1) + (6 x 0.1) + (5 x 0.01) + (4 x 0.001)

Decomposing Numbers

• Decompose the number 52.174 by 3 different ways.
  • (52 x 1) + (1 x 0.1) + (7 x 0.01) + (4 x 0.001)
  • (50 x 1) + (2 x 1) + (1 x 0.1) + (7 x 0.01) + (4 x 0.001)
  • (5 x 10) + (2 x 1) + (1 x 0.1) + (7 x 0.01) + (4 x 0.001)

Ordering Numbers

• Arrange the following decimal numbers in ascending order : 5.571, 5.729, 5.703, 5.072

  • 5.072, 5.571, 5.703, 5.729

• Arrange the following decimal numbers in descending order: 0.734, 0.192, 0.220, 0.025

  • 0.734, 0.220, 0.192, 0.025

Standard Form (2)

• Write the number > in standard form.
  • The exact number is required to answer this question.

Expanded Form (2)

• Decompose the decimal number 65.23 in expanded form
  • (6 x 10) + (5 x 1) + (2 x 0.1) + (3 x 0.01)

Price Calculations

• If the price of a pencil is 8.25 pounds. What is the price of 100 pencils of the same type?
  • 8.25 x 100 = 825 pounds

Rounding Decimals

• Round the decimal fraction 0.549 to the nearest hundredth.

  • 0.55

• Round the decimal number 5.812 to the nearest integer.

  • 6

• The temperature on a summer day is 43.7 degrees Celsius. Round the temperature to the nearest unit?

  • 44 degrees Celsius

Estimation

• Omar wants to build his entire garden fence. Estimate the length of the fence by rounding each dimension to the nearest integer.

  • 75.29 m ≈ 75 m
  • 43.56 m ≈ 44 m

• Estimate the result of the addition using the first number from the left, 15.2 + 7.5

  • 15 + 7 = 22

• Estimate the addition using your preferred strategy: 4.56 + 9.98

  • 4.56 + 9.98 ≈ 5 + 10 = 15

• Estimate the sum (to the nearest tenth) 0.85 + 2.3

  • 0.85 + 2.3 ≈ 0.9 + 2.3 = 3.2

Total Weight

• If Khalid's weight is 45.75 kg and Mahmoud's Weight is 42.5 kg, what is the total weight of Khalid and Mahmoud?
  • 45.75 + 42.5 = 88.25 kg

Money Calculations

• Ahmed has 200.5 pounds, Mahmoud has 65.75 pounds, and Adel has 88.5 pounds. How many pounds do the three have together?

  • 200.5 + 65.75 + 88.5 = 354.75 pounds

• Ahmed has 100.75 pounds and gave his brother 24.25 pounds. How much money remains with Ahmed?

  • 100.75 - 24.25 = 76.50 pounds

• What is the value of the digit 5 in the number 3.456?

  • Five-hundredths

Addition Models

• In the following model, what color represents the addition operation below and write the result: (0.7 + 0.25 = ………..)

  • The question requires a visual model to be answered.

• 5 + 0.157 = ……………

  • 5 + 0.157 = 5.157

• 0.85 + ………….= 1

  • 0.85 + 0.15 = 1

• 1 = 0.15 + 0.5 + …………..

  • 1 = 0.15 + 0.5 + 0.35

• How many hundredths are there in 0.3?

  • There are 30 hundredths in 0.3.

Subtraction Models

• In the following model, what color represents the subtraction operation below and write the result: 0.25 – 0.13= ………..

  • The question requires a visual model to be answered.
• 1. 0.235 = 0.2 + ……… + 0.005
  • 1. 0.235 = 0.2 + 0.03 + 0.005

Height Calculations

• If Ahmed's height is 1.2 meters and Khalid's height is 150 cm, what is the total height of both in meters?
  • Khalid's height: 150 cm = 1.5 meters
  • Total height: 1.2 + 1.5 = 2.7 meters

Distance Calculations

• Hassan wants to cut a road that is 80.5 kilometers long. If Hassan has already cut 3.156 km, what is the remaining distance?

  • 80.5 - 3.156 = 77.344 km

• How many hundredths are there in 0.8?

  • There are 80 hundredths in 0.8.

Mass Calculations (2)

• If the mass of the orange is 5.75 kg and the mass of the apple is 2.5 kg, what is the mass of the orange and the apple?
  • 5.75 + 2.5 = 8.25 kg

Money Calculations (2)

• Khaled had 100 L.E. He bought a book for 65.3 L.E. How much does he have left?
  • 100 - 65.3 = 34.7 L.E.

Money Calculations (3)

• Khaled had 10.75 L.E. and gave his brother 5.25 L.E., estimate the amount remained with Khaled. Using Decimals Benchmark?
  • 10.75 L.E. ≈ 11 L.E.
  • 5.25 L.E. ≈ 5 L.E.
  • 11 - 5 = 6 L.E.
  • Khaled has approximately 6 L.E left..

Subtraction with Decimals

• Find the result of subtraction 0.32-0.195 =
  • 0.32 - 0.195 = 0.125

Estimation (2)

• Estimate the result using the Front-End Estimation from the left 8.92 - 3.5=…..
  • 8 - 3 = 5

Distance Calculations (2)

• A road with a length of 98.5 km, the car traveled a distance of 35.25 km, then how many kilometers of road remain?
  • 98.5 - 35.25 = 63.25 km

Money Calculations (4)

• Khaled had 100 L.E. He bought a book for 22.5 pounds. How much does he have left?
  • 100 - 22.5 = 77.5 L.E.

Bank Deposits

• Mahmoud deposited 2,000 L.E. in a bank and added profits of 235.5 L.E How many L.E. does he have in the bank balance after adding the profits?
  • 2000 + 235.5 = 2235.5 L.E.

Subtraction with Decimals (2)

• Find the subtraction result: - 0.9 - 0.325 using Benchmark Decimals strategy
  • 0.9 ≈ 1
  • 0.325 ≈ 0.3
  • 1 - 0.3 = 0.7
  • The estimated result is 0.7

Estimation (3)

• Estimate the subtraction result by rounding to the nearest unit: 9.65 - 1.2 = …..
  • 10 - 1 = 9

Height Calculations (2)

• If Imad's height is 1.7 meters and Ahmed's height is 0.35 meters shorter than him, what is Ahmed's height?
  • 1.7 - 0.35 = 1.35 meters

Money Calculations (5)

• Khaled had 300 L.E. He bought a book for 65.25 pounds. How much does he have left?
  • 300 - 65.25 = 234.75 L.E.

Estimation (4)

• What is the estimate of subtracting 15.8 - 3.21 using the Benchmark Decimals strategy
  • 15.8 ≈ 16
  • 3.21 ≈ 3
  • 16- 3 = 13
  • The estimate is 13

Subtraction with Decimals (3)

• Find the result of the subtraction: 0.6 - 0.18 = …..
  • 0.6 - 0.18 = 0.42

Decreasing Decimals

• What is the decrease of 2.5 from 33.14
  • 33.14 - 2.5 = 30.64

Algebra Basics

• Identify the variable in the following math sentence: 56 – x = 47.5
  • The variable is x.

Writing Equations

• Write an equation that expresses this situation: Kamel bought a bag for 45.75 pounds and a pair of shoes for 36.15 pounds, what is the total amount Kamel paid?
  • Total amount = 45.75 + 36.15

Solving Equations

• Find the value of the unknown in the following equation: V + 42.89 = 100.01
  • V = 100.01 - 42.89
  • V = 57.12

Word Problems & Equations

• Write a word problem that represents the equation: f - 2.3 = 8.4 and then find the value of f.
  • A farmer harvested 8.4 kg of apples. He sold 2.3 kg of apples. How many kg of apples does he have left?
  • f = 8.4 + 2.3
  • f = 10.7

Model Based Equations

• Amjad used the bar model to find the variable k in the equation 3.2 = 5.4 – k , what is the value of the variable?
  • k = 5.4 - 3.2
  • k = 2.2