Quantitative practice

### 1.1. Quantitative practice

**Lesson 1 page 170: **Write the correct number in the dot

1 nest = … kg 1 quintal = … oats

1 quintal = … kg 1 ton = … quintal

1 ton = … kg 1 ton = … oats

**Solution guide:**

Based on the table of units of measurement:

1 nest = 10 kg 1 quintal = 10 oats

1 quintal = 100kg 1 ton = 10 quintals

1 ton = 1000kg 1 ton = 100 oats

Lesson 2 page 171: Write the correct number in the dot

a) 10 oats = …kg \(\frac{1}{2}\) oats = … kg

50kg =….oats 1 nest 8kg = …kg

b) 5 quintals =….oats 1500kg =….weights

30 oats = … 7 weights 20kg = ….kg

c) 32 tons = …..tons 4000kg = ….tons

230 quintals = …..ton 3 ton 25kg = …..kg

__Solution guide:__

- Based on the table of units of measurement.

a) 10 oats = 100kg \(\frac{1}{2}\) oats = 5kg

50kg = 5 oats 1 bird 8kg = 18kg

b) 5 quintals = 50 yen 1500kg = 15 quintals

30 yen = 3 quintals 7 quintals 20kg = 720kg

c) 32 tons = 320 quintals 4000kg = 4 tons

230 quintals = 23 tons 3 tons 25kg = 3025kg

**Lesson 3 page 171: **Put > , < , = in the dot

2kg 7 hg…2700g 60kg 7g …..6007g

5kg 3g….5035g 12 500g…..12kg 500g

__Solution guide:__

- Convert the measurements to the same unit of measure and compare the results.

+) 2kg7hg = 27hg = 2700g.

So: 2kg7hg = 2700g.

+) 60kg7g = 60 007g. Which 60 007g > 6007g.

So: 60kg 7g > 6007g.

+) 5kg3g = 5003g. That 5003g < 5035g.

So: 5kg3g < 5035g.

+) 12 500g = 12 000g + 500g = 12kg + 500g = 12kg 500g.

So 12 500g = 12kg 500g

**Lesson 4 page 171: **A fish weighs 1kg 700g, a bunch of vegetables weighs 300g. How many kilograms does both fish and vegetables weigh?

__Solution guide:__

Exchange: 1kg 700g = 1700g

Weight of both vegetables and fish = weight of bunch of vegetables + weight of fish.

Convert the result you just found to the unit of measurement of kilograms, noting that 1kg = 1000g.

*Solution*

Exchange: 1kg 700g = 1700g

Both fish and vegetables weigh in kilograms:

1700 + 300 = 2000 (g)

2000g = 2kg

Answer: 2kg.

**Lesson 5 page 171: **A car can carry 32 bags of rice, each bag weighs 50kg. How many kilograms of rice can the truck carry in all?

__Solution guide:__

- Weight of 32 bags of rice = weight of 1 bag of rice × 32.
- Convert the results you just found into the unit of measurement is weight, note that 1 quintal = 100kg

*Solution*

The car that can carry all the rice is:

50 x 32 = 1600 (kg)

1600kg = 16 quintals

Answer: 16 quintals of rice.

### 1.2. Quantitative Review (continued)

**Lesson 1 page 171:** Write the correct number in the dot

1 hour = …minutes 1 year = …months

1 minute = …seconds 1 century = … years

1 hour = …seconds 1 non-leap year = …days

1 leap year = … days

__Solution guide:__

1 hour = 60 minutes 1 year = 12 months

1 minute = 60 seconds 1 century = 100 years

1 hour = 3600 seconds 1 non-leap year = 365 days

1 leap year = 366 days

**Lesson 2 page 171:** Write the correct number in the dot

a) 5 hours = … minutes 3 hours 15 minutes = … minutes

420 seconds = … minutes \(\frac{1}{{12}}\) hours = … minutes

b) 4 minutes = … seconds 3 minutes 25 seconds = … seconds

2 hours = … seconds \(\frac{1}{{10}}\) minutes = … seconds

c) 5 centuries = … year \(\frac{1}{{20}}\) century = … year

12 centuries = … year 2000 years = … century

__Solution guide:__

a) 5 hours = 300 minutes 3 hours 15 minutes = 195 minutes

420 seconds = 7 minutes \(\frac{1}{{12}}\) hours = 5 minutes

b) 4 minutes = 240 seconds 3 minutes 25 seconds = 205 seconds

2 hours = 7200 seconds \(\frac{1}{{10}}\) minutes = 6 seconds

c) 5 centuries = 500 years \(\frac{1}{{20}}\) century = 5 years

12 centuries = 1200 years 2000 years = 20 centuries

**Lesson 3 page 172:** Put >, <, = in the dot

5 hours 20 minutes … 300 minutes \(\frac{1}{3}\) hours … 20 minutes

495 seconds … 8 minutes 15 seconds \(\frac{1}{5}\) minutes … \(\frac{1}{3}\) minutes

__Solution guide:__

5 hours 20 minutes > 300 minutes \(\frac{1}{3}\) hours = 20 minutes

495 seconds = 8 minutes 15 seconds \(\frac{1}{5}\) minutes < \(\frac{1}{3}\) minutes

**Lesson 4 page 172:** The table below shows some of Ha’s activities every morning

Time | Work |

From 6:10am to 6:30pm | Personal hygiene and exercise |

From 6:30 a.m. to 7:00 p.m | Have breakfast |

From 7:30 a.m. to 11:30 a.m | Learn and play at school |

a) How many minutes does Ha eat breakfast?

b) How long does Ha stay at school in the morning?

__Solution guide:__

a) Ha has breakfast in 20 minutes:

(6 hours 30 minutes – 6 hours 10 minutes = 20 minutes)

b) Ha is at school for 4 hours in the morning:

(11 hours 30 minutes – 7 hours 30 minutes = 4 hours)

**Lesson 5 page 172: **Which of the following time periods is the longest?

a) 600 seconds ; b) 20 minutes ; c) \(\frac{1}{4}\) hours; d) \(\frac{3}{{10}}\) hours

__Solution guide:__

We have 600 seconds = 10 minutes; \(\frac{1}{4}\) hours = 15 minutes

\(\frac{3}{{10}}\) hours = 18 minutes

Because 10 minutes < 15 minutes < 18 minutes < 20 minutes

So 20 minutes is the longest.

### 1.3. Quantitative Review (continued)

**Lesson 1 page 172: **Write the correct number in the dot

1m^{2} = … dm^{2} 1 kilometer^{2} = … m^{2}

1m^{2 }= … cm^{2 } 1dm^{2} = … cm^{2}

__Solution guide:__

- Based on the theory of units of measurement of area.

1m^{2} = 100dm^{2} 1 kilometer^{2 }= 1000000m^{2}

1m^{2} = 10000cm^{2} 1dm^{2 }= 100cm^{2}

**Lesson 2 page 172: **Write the correct number in the dot

a) 15m^{2} = … cm^{2 } \(\frac{1}{{10}}\)m^{2 }= … dm^{2}

103m^{2} = … dm^{2 } \(\frac{1}{{10}}\)dm^{2} = … cm^{2}

2110dm^{2} = … cm^{2} \(\frac{1}{{10}}\)m^{2} = … cm^{2}

b) 500cm^{2} = … dm^{2} 1cm^{2 }= … dm^{2}

1300dm^{2} = … m^{2} 1dm^{2} = … m^{2}

60000cm^{2} = … m^{2} 1cm^{2} = … m^{2}

c) 5m^{2}9dm^{2} = … dm^{2} 700dm^{2} = … m^{2}

8m^{2}50cm^{2} = … cm^{2 } 50000cm^{2 }= … m^{2}

__Solution guide:__

- Apply the way to convert some basic units:

1m^{2} = 100dm^{2} 1 kilometer^{2} = 1000000m^{2}

1m^{2 }= 10000cm^{2 } 1dm^{2} = 100cm^{2}

*Solution :*

a) 15m^{2 }= 150000cm^{2 } \(\frac{1}{{10}}\)m^{2}= 10dm^{2}

103m^{2 }= 10300dm^{2 } \(\frac{1}{{10}}\)dm^{2} = 10cm^{2}

2110dm^{2} = 211000cm^{2} \(\frac{1}{{10}}\)m^{2}= 1000cm^{2}

b) 500cm^{2} = 5dm^{2 } 1cm^{2} = \(\frac{1}{{100}}\)dm^{2}

1300dm^{2 }= 13m^{2 } 1dm^{2} = \(\frac{1}{{100}}\)m^{2}

60000cm^{2}= 6m^{2 } 1cm^{2} = \(\frac{1}{{100000}}\)m^{2}

c) 5m^{2}9dm^{2 }= 509dm^{2} 700dm^{2 }= 7m^{2}

8m^{2}50cm^{2 }= 80050cm^{2} 50000cm^{2 }= 5m^{2}

**Lesson 3 page 173: **Put the appropriate sign >, <, = in the dot

2 m^{2}5dm^{2 }… 25dm^{2 } 3m^{2}99dm^{2} … 4m^{2}

3dm^{2}5cm^{2} … 305cm^{2} 65m^{2} … 6500dm^{2}

__Solution guide:__

- Convert the area measurements to the same units and compare the results.

+) 2m^{2}5dm^{2} = 205dm^{2 }. Which 205dm^{2} > 25dm^{2}

So: 2m^{2}5dm^{2} > 25dm^{2}

- +) 3m
^{2}99dm^{2}= 399dm^{2}; 4m^{2}= 400dm^{2}. Which 399dm^{2 }< 400dm^{2}

So: 3m^{2 }99dm^{2 }< 4m^{2}

+) 3dm^{2} 5cm^{2} = 3dm^{2} + 5cm^{2} = 300cm^{2} + 5cm^{2} = 305cm^{2}

So: 3dm^{2} 5cm^{2} = 305cm^{2}

+) 65m^{2} = 6500dm^{2}

**Lesson 4 page 173: **A rectangular field is 64m long and 25m wide. On average, for every 1m2 of that field, \(\frac{1}{2}\)kg of rice can be harvested. How many kilograms of rice can be harvested in that field?

__Solution guide:__

- Calculate the area of the field = length x width.
- Calculate the number of rice harvested = the number of rice harvested per 1m
^{2}field x area of field. - Convert the results you have just found to the unit of weight, note 1 quintal = 100kg.

*Solution*

The area of the field is:

64 x 25 = 1600 (m^{2})

The number of paddy harvested in the field is:

\(\frac{1}{2}\) x 1600 = 800 (kg)

800kg = 8 quintals

Answer: 8 quintals of rice.

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