Why do we pray? Because we want to depend on God. Why do we fast? Because we do not want to depend on ourselves. Why do we pray and fast? Because we want to change our dependence from ourselves to God.
When we pray, our spirit will be strengthened. When we fast, our body will be weakened. By strengthening our spirit and weakening our body, it will be easier for us to turn our heart from our self to God. Thus, we will depend on ourselves less and on God more.
When we pray, we do not always have to fast, but when we fast, we must always pray. Why? When we pray, our spirit is made strong. As long as it is strong enough to control our body, we do not need to fast. When we fast, our body is made weak. If we do not pray, then our spirit will also be weak. A weak spirit cannot control a weak body.
What will be the difference for us if we just pray and if we pray with fasting? If we do not pray, we will only be aware of the physical realm. We will not be aware of the spiritual realm. If we pray, we will be aware both of the physical realm and the spiritual realm. If we pray and fast, our awareness of the physical realm will decrease so that we are more aware of the spiritual realm than the physical realm.
Most of the time when we pray, we pray for ourselves about the things of this world. We may pray for others, but our prayers for them will primarily be for the things of this world. We seldom pray for the things of God for them. When we pray with fasting, we will be led to pray not just for ourselves nor for the things of this world, but for others and for the things of God because it will no longer be us who pray. It will be the Holy Spirit who prays in us. We will pray by the Spirit of prayer.